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- In low-speed crash tests of five cars, the repair costs were computed for a factory authorizedrepair and an independent repair workshop. The results are listed in Table 2. Is there sufficientevidence to support the claim that the independent workshop has lower repair costs? Use a 0.01significance level.Table 2 car 1 2 3 4 5 authorized repair centre X1 RM797 RM571 RM904 RM1147 RM418 independent workshop X2 RM523 RM488 RM875 RM911 RM297 D=X1 - X2 274 83 29 236 121 D2 = (X1 -X2)2 75076 6889 841 55696 14641A statistical program is recommended. Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars). Weekly Usage(hours) AnnualMaintenanceExpense 13 17.0 10 22.0 20 30.0 28 37.0 32 47.0 17 30.5 24 32.5 31 39.0 40 51.5 38 40.0 #1) Develop the estimated regression equation that could be used to predict the annual maintenance expense (in hundreds of dollars) given the weekly usage (in hours). (Round your numerical values to two decimal places.) #2) The expected expense of a machine being used 34 hours per week is $ hundred.The marketing manager of a large super-market chain has the business objective of using shelf space most efficiently. Toward that goal, they would like to use shelf space to predict the sales of a specialty pet food. Data are collected from a random sample of 12 equal-sized store, with the following results: Shelf Space Sales Aisle Location 5 160 0 5 220 1 5 140 0 10 190 0 10 240 0 10 260 1 15 230 0 15 270 0 15 280 1 20 260 0 20 290 0 20 310 1 For these data, Syx = 30.8058436 and hi = 0.1373333 when X = 8. *Round final answers below to three decimal places. Do not round calculations until the final answer. (a) Construct a 95% confidence interval estimate of the mean weekly sales for all stores that have 8 square feet of shelf space for pet food. (b) Construct a 95% prediction interval of the weekly sales of an individual store that has 8 square feet of shelf…
- A consumer group, concerned about the mean fat content of a certain grade of ground beef, submits a random sample 12 packets of ground beef for analysis, to an independent laboratory. The percentage of fat from each packet is as follows Sample Percentage of Fat 1 21 2 18 3 19 4 16 5 18 6 24 7 22 8 19 9 24 10 14 11 18 12 15 The manufacturer claims that the mean fat content for this grade of ground beef is less than 20%. Assuming that the percentage fat content is normally distributed with a standard deviation of 3, conduct the appropriate hypothesis test and advise the consumer group about the validity of the manufacturer’s claim.A newsletter rates mutual funds. Independent random samples of 10 funds with the highest rating and 10 funds with the lowest rating were chosen. The following figures are percentage rates of return achieved by these 20 funds in the next year.Highest rated 8.1 12.7 13.9 2.3 16.1 5.4 7.3 9.8 14.3 4.1Lowest rated 3.5 14.0 11.1 4.7 6.2 13.3 7.0 7.3 4.6 10.0Test the null hypothesis of no difference between the central locations of the population distributions of rates of return against the alternative that the highestrated funds tended to achieve higher rates of return than the lowest-rated funds.A low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. (10)b) A CDC press release publishing the results of this study claims that…
- A low-level CDC bureaucrat wants to please his boss by gathering evidence thatthe current government-mandated shutdown of society is not causing people’s mentalhealth to deteriorate, so that it can safely be continued for several years if anyexpert says it’s necessary.He polls a random sample of 1600 citizens, gathering data on such items asincome loss, weight gain, access to toilet paper, hours spent binge-watchingNetflix, and number of injuries caused by household fights, and compiles all thisinto a scientifically-weighted “misery index”.The mean misery index from the sample is 99.2; it seems reasonable to use apopulation standard deviation σ = 19.1.a) Does this information provide significant evidence (at the 5% level) that thenationwide mean misery index is less than 100? Set up appropriate null andalternative hypotheses, calculate the appropriate test statistic, find the P-value,and state your conclusion. b) A CDC press release publishing the results of this study claims that…The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers? Teacher 1 Teacher 2 xbar = 473 xbar = 459 S1= 39.7 S2 = 24.5 n1 = 8 n2 = 18 Identify the rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using critical values.The manager of a company that assembles and exports a particular type of pumps wants to know if there is a link between the number of hours spent by assembly workers in training and their productivity on the job. A random sample of 7 assembly workers was selected and their performances evaluated. The summary of the obtained data is listed in Table 2. Table 2: Shows the time spend by workers during training and their productivity on jobTraining hours (x) 20 36 20 38 40 33 32Output (y) 40 70 44 56 60 48 62 (i) Construct a scatter plot of the sample data and comment on the relationship between hours of training and output. (ii) Estimate a simple regression line, using the method of least squares, to identify a linear relationship between the hours of training received by assembly workers and their output (i.e. number of units assembled per day). (iii) Interpret, in context, the gradient/slope of the regression line. (iv) Estimated the output at 20 hours training time. (v) Interpret the…
- Consider the following table containing yields for mutual funds in different asset classes (small, mid, and large cap). Use a one-way ANOVA test to determine if there is a difference between the mean yields for the three asset classes, at the 0.05 level of significance. Assume the population distributions are approximately normal with equal population variances. Fund Yield by Asset Class SMALL CAP MID CAP LARGE CAP Small Cap Mid Cap Fund Yield (%) Fund Yield (%) Fund Yield (%) Explorer Value 2.21 Capital Value 0.95 Equity Income 3.16 Small-Cap Value Index Admiral 2.49 Mid-Cap Value Index Admiral 0.51 High Dividend Yield Index 3.59 Small-Cap Index Admiral Shares 2.03 Extended Market Index Admiral Shares 1.12 500 Index Admiral Shares 0.61 Strategic Small-Cap Equity 1.99 Mid-Cap Index Admiral Shares 1.47 Diversified Equity 1.32 Explorer 2.24 Mid-Cap Growth 1.39 FTSE Social Index 1.43 Small-Cap Growth Index…The following are the ratings of males by females in an experiment involving speed dating. Use the given data to construct a boxplot and identify the 5-number summary. 2.0 2.0 3.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.5 6.0 6.0 6.0 6.0 6.5 7.5 8.5 9.0 Question content area bottom Part 1 The 5-number summary is enter your response here, enter your response here, enter your response here, enter your response here, and enter your response here. (Use ascending order. Type integers or decimals. Do not round.)In the article “The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range” (Journal of Herpetology, Vol. 29, No. 3, pp. 391–398), Blem and Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of 44 female cottonmouths yielded a sample mean of ??̅ = 7.6 young per litter. Assume σ = 2.4. a. Is the sample mean likely to equal μ exactly? Explain your answer b. Find the 95% Confidence Interval. c. How large a sample would be needed to get at 99% confidence interval with a margin of error of just 0.1?