MATH 533 Final Exam (2017 version) - studentland [PDF]

If x is a binomial random​ variable, calculate mu, sigma squared, and sigma for each of the following values of n and

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MATH 533 Final Exam (2017 version)

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1) In one university, language professors incorporated a 10-week extensive reading program to improve students' Japanese reading comprehension. The professors collected 270 books originally written for Japanese children and required their students to read at least 40 of them as part of the grade in the course. The books were categorized into reading levels (color-coded for easy selection) according to length and complexity. Complete parts a through c. Reading Level Number Level 1 red 40 Level 2 blue 73 Level 3 yellow 51 Level 4 pink 88 Level 5 orange 15 Level 6 green 3 Total 270 a. Compute the relative frequencies in each category. Reading Level Relative Frequency Level 1 (Red) Level 2 (Blue) Level 3 (Yellow) Level 4 (Pink) Level 5 (Orange) Level 6 (Green) (Round to the nearest thousandth as needed.) I have to complete b and c because they are graphs and I don’t have time to send to you. 2.) I have to complete. It’s a graph. 3.) Consider the following sample of five measurements. 3, 5, 5, 1, 6 a. Calculate the range, s squared, and s. range= s squared = (Round to one decimal place as needed.) S = (Round to two decimal places as needed.) b. Add 3 to each measurement and repeat part a. range = s squared = (Round to one decimal place as needed.) S = (Round to two decimal places as needed.) c. Subtract 5 from each measurement and repeat part a. range = s squared = (Round to one decimal place as needed.) S = (Round to two decimal places as needed.) d. Considering your answers to parts a, b, and c, what seems to be the effect on the variability of a data set by adding the same number to or subtracting the same number from each measurement? A. There is no effect on the variability. B. The variability is decreased by the amount subtracted from each measurement. C. The variability is increased by the amount added to each measurement. D. The variability is multiplied by the amount added to or subtracted from each measurement. 4.) For two events, A and B, P(A)equals 0.4, P(B)equals 0.2, and P(A|B)equals 0.5. a. Find P(Aintersect B). b. Find P(B|A). a. P(AintersectB)= ____(Simplify your answer.) b. P(B|A) = ____(Simplify your answer.) 5.) For two independent events, A and B, P(A)equals. 6 and P(B)equals. 1. a. Find P(AintersectB). b. Find P(A|B). c. Find P(AunionB). a. P(AintersectB)= ____ b. P(A|B)= ____ c. P(AunionB)= ___ 6.) If x is a binomial random variable, calculate mu, sigma squared, and sigma for each of the following values of n and p. Complete parts a through f. a. nequals 28, pequals 0.5 mu = _____ (Round to the nearest tenth as needed.) sigma square= ____ (Round to the nearest hundredth as needed.) sigma = ____ (Round to the nearest thousandth as needed.) b. nequals 77, pequals 0.1 mu = ____ (Round to the nearest tenth as needed.) sigma squared = ____ (Round to the nearest hundredth as needed.) sigma = ____ (Round to the nearest thousandth as needed.) c. nequals 97, pequals 0.6 mu = ____ (Round to the nearest tenth as needed.) sigma squared = _____(Round to the nearest hundredth as needed.) sigma = _____(Round to the nearest thousandth as needed.) d. nequals 69, pequals 0.9 mu = _______________(Round to the nearest tenth as needed.) sigma squared = ____(Round to the nearest hundredth as needed.) sigma = ____(Round to the nearest thousandth as needed.) e. nequals 63, pequals 0.8 mu = ____(Round to the nearest tenth as needed.) sigma squared = ________ (Round to the nearest hundredth as needed.) sigma = ____(Round to the nearest thousandth as needed.) f. nequals 1, 000, pequals 0.07 Mu = ___(Round to the nearest tenth as needed.) sigma squared = ____(Round to the nearest hundredth as needed.) sigma = ____(Round to the nearest thousandth as needed.) 7.) Many primary care doctors feel overworked and burdened by potential lawsuits. In fact, a group of researchers reported that 57% of all general practice physicians do not recommend medicine as a career. Let x represent the number of sampled general practice physicians who do not recommend medicine as a career. Complete parts a through d. a. Explain why x is approximately a binomial random variable. A. The experiment consists of n identical, dependent trials, with more than two possible outcomes. The probability that an event occurs varies from trial to trial. B. The experiment consists of n identical, dependent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). C. The experiment consists of n identical, independent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S remains the same from trial to trial. The variable x is the number of S's in n trials. D. The experiment consists of n identical, independent trials, where there are only two possible outcomes, S (for Success) and F (for Failure). The probability of S varies from trial to trial. The variable x is the number of F's in n trials. b. Use the researchers' report to estimate p for the binomial random variable. P = ____ (Type an integer or a decimal.) c. Consider a random sample of 28 general practice physicians. Use p from part b to find the mean and standard deviation of x, the number who do not recommend medicine as a career. Mu = ____ (Round to two decimal places as needed.) Sigma = ___ (Round to three decimal places as needed.) d. For the sample of part c, find the probability that at least one general practice physician does not recommend medicine as a career. P(xgreater than or equals1) = _____(Round to three decimal places as needed) 8.) Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university's Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, "if you have this tendency, consider using a normal distributionlong dash 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable." Suppose you are rating an employee's performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 46 and a standard deviation of 16. Complete parts a and b. a. What is the lowest rating you should give to an "exemplary" employee if you follow the university's HR guidelines? ____ (Round to two decimal places as needed.) b. What is the lowest rating you should give to a "competent" employee if you follow the university's guidelines? _____ (Round to two decimal places as needed.) 9.) Personnel tests are designed to test a job applicant's cognitive and/or physical abilities. A particular dexterity test is administered nationwide by a private testing service. It is known that for all tests administered last year, the distribution of scores was approximately normal with mean 76 and standard deviation 8.3. a. A particular employer requires job candidates to score at least 80 on the dexterity test. Approximately what percentage of the test scores during the past year exceeded 80? b. The testing service reported to a particular employer that one of its job candidate's scores fell at the 98th percentile of the distribution (i.e., approximately 98 % of the scores were lower than the candidate's, and only 2% were higher). What was the candidate's score? a. Approximately ____% of the test scores during the past year exceeded 80. (Round to one decimal place as needed.) b. The candidate's score was ___. (Round to the nearest whole number as needed.) 10.) Suppose a random sample of nequals 16 measurements is selected from a population with mean mu and standard deviation sigma. For each of the following values of mu and sigma, give the values of mu Subscript x overbar and sigma Subscript x overbar Baseline .

1. a. Mu equals10, sigma equals5 2. b. Mu equals100, sigma equals16 3. c. Mu equals20, sigma equals16 4. d. Mu equals10, sigma equals88 5. a. mu Subscript x overbar = ___ sigma Subscript x overbar = ___ (Type an integer or a decimal.) 6. b. mu Subscript x overbar= ____ sigma Subscript x overbar= ___(Type an integer or a decimal.) 7. c. mu Subscript x overbarb= ___ sigma Subscript x overbar= ____(Type an integer or a decimal.) 8. d. mu Subscript x overbar = ____ sigma Subscript x overbar = ____(Type an integer or a decimal.) 11.) A random sample of nequals 100 observations is selected from a population with mu equals31 and sigma equals 23. Approximate the probabilities shown below. a. P(x overbar greater than or equals 28) b. P(22.1less than or equals x overbarless than or equals 26.8) c. P(x overbar less than or equals 28.2) d. P(x overbar greater than or equals27.0) a. P(x overbar greater than or equals28)= ___(Round to three decimal places as needed.) b. P(22.1less than or equals x overbarless than or equals26.8) = ____(Round to three decimal places as needed.) c. P(x overbar less than or equals28.2)= ____(Round to three decimal places as needed.) d. P(x overbargreater than or equals27.0) = ____(Round to three decimal places as needed.) 12.) The average salary for a certain profession is $70, 000. Assume that the standard deviation of such salaries is $27,500. Consider a random sample of 74 people in this profession and let x overbar represent the mean salary for the sample.

1. a. What is mu Subscript x overbar? mu Subscript x overbar = ____ 2. b. What is sigma Subscript x overbar? sigma Subscript x overbar = ___(Round to two decimal places as needed.). Describe the shape of the sampling distribution of x overbar. A. The shape is that of a uniform distribution. B. The shape is that of a poisson distribution. C. The shape is that of a normal distribution. D. The shape is that of a binomial distribution. d. Find the z-score for the value x overbar equals 61, 500. Z= ___ (Round to two decimal places as needed.)

1. e. Find Upper P left parenthesis x overbar greater than 61,500 right parenthesis. Upper P left parenthesis x overbar greater than 61,500 right parenthesis = ___(Round to three decimal places as needed.) 13.) The random sample shown below was selected from a normal distribution. 4, 5, 7, 6, 7, 7 Complete parts a and b a. Construct a 90 % confidence interval for the population mean mu. (___,___) (Round to two decimal places as needed.) b. Assume that sample mean x overbar and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n equals25 observations. Repeat part a. What is the effect of increasing the sample size on the width of the confidence intervals? The confidence interval is (____, ____). (Round to two decimal places as needed.) 14.) A newspaper reported on the results of an opinion poll in which adults were asked what one thing they are most likely to do when they are home sick with a cold or the flu. In the survey, 64% said that they are most likely to sleep and 10% said that they would watch television. Although the sample size was not reported, typically opinion polls include approximately 1,000 randomly selected respondents.

1. a. Assuming a sample size of 1,000 for this poll, construct a 95% confidence interval for the true percentage of all adults who would choose to sleep when they are at home sick. The 95% confidence interval is (____,_____). (Round to the nearest hundredth as needed.) b. If the true percentage of adults who would choose to sleep when they are at home sick is 72%, would you be surprised? Yes or No 15.) A company tests all new brands of golf balls to ensure that they meet certain specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine. Suppose the company wishes to estimate the mean distance for a new brand to within 1.5 yards with 90% confidence. Assume that past tests have indicated that the standard deviation of the distances the machine hits golf balls is approximately 10n yards. How many golf balls should be hit by the machine to achieve the desired accuracy in estimating the mean? The machine should hit ____ golf balls to achieve the desired accuracy in estimating the mean.(Round up to the nearest golf ball.) 16.) The final scores of games of a certain sport were compared against the final point spreads established by oddsmakers. The difference between the game outcome and point spread (called a point-spread error) was calculated for 220 games. The sample mean and sample standard deviation of the point-spread errors are x overbar equals1.1 and sequals 13.1. Use this information to test the hypothesis that the true mean point-spread error for all games is larger than 0. Conduct the test at alpha equals0.10 and interpret the result. Determine the null and alternative hypotheses. Choose the correct answer below.

1. A. Upper H 0: mu 0 equals0Upper H Subscript a: mu 0 not equals0 2. B. Upper H 0: mu 0 equals0Upper H Subscript a: mu 0 less than0 3. C. Upper H 0: mu 0 equals0Upper H Subscript a: mu 0 greater than0 4. D. Upper H 0 : mu 0 not equals0Upper H Subscript a: mu 0 equals0 Find the test statistic. Z = ___ (Round to two decimal places as needed.) Determine the rejection region. Choose the correct answer below. A. zgreater than 1.645 B. zgreater than 1.28 C. zgreater than 1.645 or zless than minus1.645 D. zgreater than 1.28 or zless than minus1.28 E. zless than minus1.28 F. zless than minus1.645 What is the appropriate conclusion at alpha equals0.10?

1. A. Reject H0. There is insufficient evidence to conclude that the true mean point-spread error for all games is larger than 0. 2. B. Do not reject H0. There is sufficient evidence to conclude that the true mean point-spread error for all games is larger than 0. 3. C. Reject H0. There is sufficient evidence to conclude that the true mean point-spread error for all games is larger than 0. 4. D. Do not reject H0. There is insufficient evidence to conclude that the true mean point-spread error for all games is larger than 0. 17.) When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. Tests on a sample of 12 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of x overbar equals5.53 Mpa and a standard deviation of sequals 0.33 Mpa. Orthodontists want to know if the true mean breaking strength is less than 6.07 Mpa, the mean breaking strength of the composite adhesive. a. Set up the null and alternative hypotheses for the test. Choose the correct answer below. A. Upper H 0: mu equals5.53 vs. Upper H Subscript a: mu not equals5.53 B. Upper H 0 : mu equals6.07 vs. Upper H Subscript a: mu less than6.07 C. Upper H 0: mu equals5.53 vs. Upper H Subscript a: mu less than5.53 D. Upper H 0: mu greater than or equals6.07 vs. Upper H Subscript a: mu less than6.07 E. Upper H 0: mu equals6.07 vs. Upper H Subscript a: mu greater than6.07 F. Upper H 0: mu equals6.07 vs. Upper H Subscript a: mu not equals6.07 b. Find the rejection region for the test using alpha equals0.05. Choose the correct answer below. A. t less than minus 2.201 B. t less than minus 1.796 C. t greater than 1.796 D.t less than 1.796 E. t greater than minus 1.796 F. t less than 2.201 G. t greater than 2.201 H. t greater than minus 2.201 Compute the test statistic. T = __ (Round to two decimal places as needed.) d. Give the appropriate conclusion for the test. Choose the correct answer below. A. Reject Upper H 0. There is sufficient evidence to indicate mu less than6.07 Mpa. B. Do not reject Upper H 0. There is insufficient evidence to indicate mu less than6.07 Mpa. C. Reject Upper H 0. There is insufficient evidence to indicate mu less than6.07 Mpa. D. Do not reject Upper H 0. There is sufficient evidence to indicate mu less than6.07 Mpa. e. What conditions are required for the test results to be valid? A. We must assume that the sample was not random and selected from a population with a highly skewed distribution. B. We must assume that the sample was random and selected from a population with a distribution that is approximately normal. C. We must assume that the sample was not random and selected from a normally distributed population. D. We must assume that the sample was random and selected from a population that is highly skewed. 18.) A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2, 707 firms, 697 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 28%? Use alpha equals0.10 to make your decision. What are the hypotheses for this test?

1. A. H0: pless than 0.28Ha: pequals 0.28 2. B. Upper H 0 : p equals 0.28 Upper H Subscript a Baseline : p less than 0.28 3. C. H0: pequals 0.28Ha: pnot equals 0.28 4. D. H0: pequals 0.28Ha: pgreater than 0.28 5. E. H0: pnot equals 0.28Ha: pequals 0.28 6. F. H0: pgreater than 0.28Ha: pless than or equals 0.28 What is the rejection region? Select the correct choice below and fill in the answer box(es) to complete your choice. Round to two decimal places as needed.)

1. A. zgreater than ____ 2. B. zless than ___ 3. C. zless than ___ or zgreater than ___ Calculate the value of the z-statistic for this test. Z = ____ (Round to two decimal places as needed.) What is the conclusion of the test? DO NOT REJECT OR REJECT the null hypothesis because the test statistic IS OR IS NOT in the rejection region. Therefore, there is INSUFFICIENT OR SUFFICIENT evidence at the 0.10 level of significance to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 28%. 19.) If you pay more in tuition to go to a top business school, will it necessarily result in a higher probability of a job offer at graduation? Let yequals percentage of graduates with job offers and xequals tuition cost; then fit the simple linear model, Upper E left parenthesis y right parenthesis equals beta 0 plus beta 1 x, to the data below. Is there sufficient evidence (at alpha equals0.10) of a positive linear relationship between y and x? School Annual tuition ($) % with job offer 1 39,836 99 2 39,581 99 3 39,138 85 4 38,846 89 5 38,799 98 6 38,569 912 7 38,124 89 8 37,239 97 9 37,115 86 10 36,345 98 Give the null and alternative hypotheses for testing whether there exists a positive linear relationship between y and x?

1. A. Upper H 0: beta 0 equals 0 Upper H Subscript a: beta 0 less than 0 2. B. Upper H 0 : beta 1 equals 0 Upper H Subscript a: beta 1 greater than 0 3. C. Upper H 0 : beta 0 equals 0 Upper H Subscript a: beta 0 not equals0 4. D. Upper H 0: beta 1 equals 0 Upper H Subscript a: beta 1less than0 5. E. Upper H 0 : beta 1 equals 0 Upper H Subscript a: beta 1 not equals 0 6. F. Upper H 0: beta 0 equals 0 Upper H Subscript a : beta 0 greater than0 Find the test statistic. T ____(Round to two decimal places as needed.) Find the p-value. p-value = ___(Round to four decimal places as needed.) Make the appropriate conclusion at alpha equals0.10. Choose the correct answer below.

1. A. Do not reject Upper H 0. There is sufficient evidence that there exists a positive linear relationship between y and x.

1. B. Do not reject Upper H 0. There is insufficient evidence that there exists a positive linear relationship between y and x. 2. C. Reject Upper H 0. There is sufficient evidence that there exists a positive linear relationship between y and x. 3. D. Reject Upper H 0. There is insufficient evidence that there exists a positive linear relationship between y and x. 20.) I have to come back to this. It’s a few graphs. 21.) Suppose you fit the first-order multiple regression model y equalsbeta 0 plus beta 1 x 1 plus beta 2 x 2 plus epsilon to n equals 25 data points and obtain the prediction equation ModifyingAbove y with caret equalsnegative 68.73 plus 9.32 x 1 plus 4.92 x 2. The estimated standard deviations of the sampling distributions of beta 1 and beta 2 are 1.26 and 0.63, respectively. a. Test Upper H 0 : beta 1 equals 0 against Upper H Subscript a Baseline : beta 1 not equals 0. Use alpha equals0.01. b. Find a 95% confidence interval for beta 2. Interpret the interval. a. The test statistic is _____. (Round to three decimal places as needed.) The p-value is ___ (Round to three decimal places as needed.) DO NOT REJECT OR REJECT the null hypothesis. There IS OR IS NOT sufficient evidence to support the alternative hypothesis. b. What is the confidence interval? (____,____)(Round to three decimal places as needed.) Interpret this interval. We are ___% confident that the true value of beta 2 lies in this interval. (Type a whole number.) 22.) Suppose a statistician built a multiple regression model for predicting the total number of runs scored by a baseball team during a season. Using data for nequals 200 samples, the results below were obtained. Complete parts a through d. Ind. Var. B estimate Standard error Ind. Var. estimate Standard error Intercept 3.56 18.11 Doubles (x3) 0.66 0.03 Walks (x1) 0.24 0.03 Triples (x4) 1.08 0.24 Singles (x2) 0.52 Home runs (x5) 1.59 0.05 a. Write the least squares prediction equation for yequals total number of runs scored by a team in a season. ModifyingAbove y with caret equals nothing plus left parenthesis nothing right parenthesis x 1 plus left parenthesis nothing right parenthesis x 2 plus left parenthesis nothing right parenthesis x 3 plus left parenthesis nothing right parenthesis x 4 plus left parenthesis nothing right parenthesis x 5 (Type integers or decimals.) b. Interpret, practically, ModifyingAbove beta with caret 0 and ModifyingAbove beta with caret 1 in the model. Which statement below best interprets ModifyingAbove beta with caret 0?

1. A. For a change of ModifyingAbove beta with caret 0 in any variable, the runs scored decreases by 1. 2. B. For an increase of 1 in any variable, the runs scored changes by ModifyingAbove beta with caret 0. 3. C. For a change of ModifyingAbove beta with caret 0 in any variable, the runs scored increases by 1. 4. D. For a decrease of 1 in any variable, the runs scored changes by ModifyingAbove beta with caret 0. 5. E. This parameter does not have a practical interpretation. Which statement below best interprets ModifyingAbove beta with caret 1?

1. A. For a change of ModifyingAbove beta with caret 1 in the number of walks, the runs scored increases by 1. 2. B. For an increase of 1 in the number of walks, the runs scored changes by ModifyingAbove beta with caret 1. 3. C. For a change of ModifyingAbove beta with caret 1 in the number of walks, the runs scored decreases by 1. 4. D. For a decrease of 1 in the number of walks, the runs scored changes by ModifyingAbove beta with caret 1. 5. E. This parameter does not have a practical interpretation. c. Conduct a test of Upper H 0 : beta 1 equals 0 against Upper H Subscript a Baseline : beta 1 greater than 0 at alpha equals0.01. The test statistic is ____ . (Round to three decimal places as needed.) The p-value is ___. (Round to three decimal places as needed.) REJECT OR DO NOT REJECT the null hypothesis. There IS OR IS NOT sufficient evidence to support the alternative hypothesis. d. Form a 90% confidence interval for beta 4. Interpret the results. (___,____) (Round to three decimal places as needed.) Interpret this interval. We are ____% confident that the true value of beta 4 lies in this interval. (Type a whole number.) 23.) For this problem, use the multiple regression equation below to complete parts (a) and (b). ModifyingAbove Upper Y with caret Subscript i Baseline equals 10 plus 5 Upper X Subscript 1 i Baseline plus 3 Upper X Subscript 2 i a. Interpret the meaning of the slopes. A. If Upper X 2 is constant, when Upper X 1 increases one unit, Y increases 3 units. If Upper X 1 is constant, when Upper X 2 increases one unit, Y increases 5 units. B. If Upper X 1 increases one unit, Y increases 3 units. If Upper X 2 increases one unit, Y increases 5 units. C. If Upper X 1 increases one unit, Y increases 5 units. If Upper X 2 increases one unit, Y increases 3 units. D. If Upper X 2 is constant, when Upper X 1 increases one unit, Y increases 5 units. If Upper X 1 is constant, when Upper X 2 increases one unit, Y increases 3 units. b. Interpret the meaning of the Y-intercept. A. The Y-intercept 5 is the estimate of the mean value of Y if Upper X 1 is 0. B. The Y-intercept 10 is the estimate of the mean value of Y if Upper X 1 is 0. C. The Y-intercept 5 is the estimate of the mean value of Y if Upper X 1 and Upper X 2 are both 0. D. The Y-intercept 10 is the estimate of the mean value of Y if Upper X 1 and Upper X 2 are both 0. 24.) Given the estimated linear model shown below, complete the following computations. ModifyingAbove y with caret equals10 plus 3 x 1 plus 4 x 2 plus 2 x 3 a. Compute ModifyingAbove y with caret when x 1 equals 11 comma x 2 equals 14 comma and x 3 equals 35. b. Compute ModifyingAbove y with caret when x 1 equals 20 comma x 2 equals 24 comma and x 3 equals 12. c. Compute ModifyingAbove y with caret when x 1 equals 31 comma x 2 equals 32 comma and x 3 equals 19. d. Compute ModifyingAbove y with caret when x 1 equals 33 comma x 2 equals 35 comma and x 3 equals 26. a. ModifyingAbove y with caret = ____ b. ModifyingAbove y with caret = ___ c. ModifyingAbove y with caret = ___ d. ModifyingAbove y with caret = ____ 25.) The accompanying regression table shows a regression of MSRP (manufacturer's suggested retail price) on both Displacement and Bore for off-road motorcycles. Both of the predictors are measures of the size of the engine. The displacement is the total volume of air and fuel mixture that an engine can draw in during one cycle. The bore is the diameter of the cylinders. Complete parts (a) and (b) below. Regression Table Dependent variable is MSRP R squared= 75.9% r squared (adjusted) = 77.5% S = 979.8 with 98 -3 = 95 degrees of freedom variable coeff se (coeff) t ratio pvalue Intercept 314.259 1006 0.312 0.7554 Bore 40.6143 25.92 1.57 0.1205 Displacement 6.28151 3.837 1.64 0.1049 a) State and test the standard null hypothesis for the coefficient of Bore. What are the null and alternative hypotheses?

1. A. Upper H 0: beta Subscript Bore equals 0 Upper H Subscript Upper A: beta Subscript Bore not equals 0 2. B. Upper H 0: beta Subscript Bore equals 0 Upper H Subscript Upper A: beta Subscript Boreless than 0 3. C. Upper H 0: beta Subscript Bore equals 0 Upper H Subscript Upper A: beta Subscript Bore greater than 0 4. D. Upper H 0: beta Subscript Bore not equals 0 Upper H Subscript Upper A: beta Subscript Bore equals0 Determine the test statistic. T = ____ (Type an integer or a decimal.) Determine the P-value. P-value = ___(Type an integer or a decimal.) Assume alphaequals0.05. What is the proper conclusion? REJECT OR FAIL TO REJECT HO. There is SUFFICIENT OR NOT SUFFICIENT Evidence that Bore has a coefficient that is DIFFERENT THAN ZERO, LESS THAN ZERO, GREATER THAN ZERO, OR EQUAL TO ZERO. b) Both of these predictors seem to be linearly related to MSRP. Explain what the result in (a) means. Choose the correct answer below. A. Bore has a coefficient that is clearly different from zero but does not contribute in the multiple regression to predicting MSRP. B. Bore has a coefficient that is not clearly different from zero but does contribute in the multiple regression to predicting MSRP. C. Although Bore might be individually significant in predicting MSRP, in the multiple regression, it does not add enough to the model to have a coefficient that is clearly different from zero. D. Bore has a coefficient that is clearly different from zero and is significant in predicting MSRP in the multiple regression. 26.) Based on a random sample of 1040 adults, the mean amount of sleep per night is 8.51 hours. Assuming the population standard deviation for amount of sleep per night is 1.7 hours, construct and interpret a 90% confidence interval for the mean amount of sleep per night. A 90% confidence interval is (____,___). (Round to two decimal places as needed.) Interpret the confidence interval.

1. A. There is a 90% chance that the true value of the mean will equal the mean of the interval. 2. B. There is a 90% chance that the true value of the mean will not equal the mean of the interval. 3. C. We are 90% confident that the interval actually does contain the true value of the mean. 4. D. We are 90% confident that the interval actually does not contain the true value of the mean. 27.) The accompanying data in the table below were derived from life tests for two different brands of cutting tools. Complete parts a through c. Data table Cutting speed (meters per minute) Useful life (hours) Brand A Brand B 30 4.8 6.2 30 4.4 6.6 30 5.3 5.2 40 4.6 5.0 40 4.2 4.4 40 2.5 5.0 50 4.4 4.5 50 2.8 4.0 50 1.0 3.7 60 4.0 3.8 60 2.0 3.0 60 1.1 2.4 70 1.1 1.5 70 0.5 2.0 70 3.0 1.0 a. Use a 90% confidence interval to estimate the mean useful life of a brand A cutting tool when the cutting speed is 45 meters per minute. Repeat for brand B. Compare the widths of the two intervals and comment on the reasons for any difference. The mean useful life of a brand A cutting tool when the cutting speed is 45 meters per minute is____to ___ hours. (Round to one decimal place as needed.) The mean useful life of a brand B cutting tool when the cutting speed is 45 meters per minute is ___to ____ hours. (Round to one decimal place as needed.) Compare the widths of the two intervals and comment on the reasons for any difference. Choose the correct answer below. The mean useful life of a brand B cutting tool when the cutting speed is 45 meters per minute is ____to ____ hours. (Round to one decimal place as needed.) Compare the widths of the two intervals and comment on the reasons for any difference. Choose the correct answer below.

1. A. Brand B is wider than brand A. The value of t Subscript alpha divided by 2is different for the two intervals. 2. B. Brand A is wider than brand B. The value of ModifyingAbove y with caret is different for the two intervals. 3. C. Brand A is wider than brand B. The estimated standard error of ModifyingAbove y with caret is different for the two intervals. 4. D. There is no difference in the widths of the two intervals.

1. b. Use a 90% prediction interval to predict the useful life of a brand A cutting tool when the cutting speed is 45 meters per minute. Repeat for brand B. Compare the widths of the two intervals to each other and to the two intervals you calculated in part a. Comment on the reasons for any difference.The predicted useful life of a brand A cutting tool when the speed is 45 meters per minute is ____ to _____hours.(Round to one decimal place as needed.) The predicted useful life of a brand B cutting tool when the speed is 45 meters per minute is ___ to ___ hours. (Round to one decimal place as needed.) Compare the widths of the two intervals to each other. Choose the correct answer below.

1. A. The prediction interval for brand A is larger than the prediction interval for brand B because the estimated standard error of ModifyingAbove y with caretis different for the two intervals. 2. B. The prediction interval for brand B is larger than the prediction interval for brand A because the value of ModifyingAbove y with caret is different for the two intervals. 3. C. The prediction intervals are the same size. Compare the widths of the two prediction intervals to the two confidence intervals you calculated in part a. Choose the correct answer below. A. The prediction intervals are both smaller than the corresponding confidence intervals. B. The prediction intervals are both larger than the corresponding confidence intervals. C. The two prediction intervals are the same size as the corresponding confidence intervals. D. There is no difference in the widths of the four intervals. Comment on the reasons for any difference. Choose the correct answer below.

1. A. The value of t Subscript alpha divided by 2 for the estimated mean value of y is smaller than the value of t Subscript alpha divided by 2 for the predicted value of y. B. The standard error for the estimated mean value of y is smaller than the standard error for the predicted value of y. C. The standard error for the estimated mean value of y is larger than the standard error for the predicted value of y. D. The value of t Subscript alpha divided by 2 for the estimated mean value of y is larger than the value of t Subscript alpha divided by 2 for the predicted value of y. c. Suppose you were asked to predict the useful life of a brand A cutting tool for a cutting speed of xequals 100 meters per minute. Because the given value of x is outside the range of the sample x-values, the prediction is an example of extrapolation. Predict the useful life of a brand A cutting tool that is operated at 100 meters per minute and construct a 90% prediction interval for the actual useful life of the tool. What additional assumption do you have to make in order to ensure the validity of an extrapolation? The predicted useful life of a brand A cutting tool that is operated at 100 meters per minute is ____ to ____. (Round to two decimal places as needed.) The actual predicted useful life of a brand A cutting tool when the speed is 100 meters per minute is ____ to ____ hours. (Round to one decimal place as needed.) What additional assumption do you have to make in order to ensure the validity of an extrapolation?

1. A. The value of t Subscript alpha divided by 2 can be found for xequals 100. 2. B. The linear regression is an accurate model when xequals 100. 3. C. There is no additional assumption required.

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