In its 2016 Auto Reliability Survey, Consumer Reports asked subscribers to report their maintenance and repair costs. Most individuals are aware of the fact that the average annual repair cost for anautomobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26automobiles 4 years old showed a sample standard deviation for annual repair costs of $190 and a sample of 24 automobiles 2 years old showed a sample standard deviation for annual repair costs of$100.a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles. Let 4 year old automobiles be represented by population1.0²Ho o less than or equal toH₁: ogreater thanb. At a 0.01 level of significance, what is your conclusion?Calculate the value of the test statistic (to 2 décimals).ⓇThe p-value is less than 0.01ConcludeUse Table 4 of Appendix B.that 4 year old automobiles have a larger variance in annual repair costs compared to 2 year old automobiles.

a. Suppose the population variance of annual repair cost for the 4 years old automobiles is σ12 and…

Answered: In its 2016 Auto Reliability Survey,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of two jobs per 8-hour day. The company's repair facility is a single - server system operated by a repair technician. The service time varies, with a mean repair time of 3.2 hours and a standard deviation of 2.0 hours. The company's cost of the repair operation is $27 per hour. In the economic analysis of the waiting line system, Robotics uses $37 per hour cost for customers waiting during the repair process. (a) What are the arrival rate and service rate in jobs per hour? (Round your answers to four decimal places.) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) The company is considering purchasing a computer-based equipment repair system that would enable a constant repair time of 3.2 hours.…
Insurance Company A claims that its customers pay less for car insurance, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 13 people who buy insurance from Company A, the mean cost is $⁢150 per month with a standard deviation of $⁢19. For 9 randomly selected customers of Company B, you find that they pay a mean of $⁢157 per month with a standard deviation of $16. Assume that both populations are approximately normal and that the population variances are equal to test Company A’s claim at the 0.05 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places. Step 3 of 3: Draw a conclusion and interpret the decision.
The Wall Street Journal reported that approximately 25% of the people who are told a product is improved will believe that it is in fact improved. The remaining 75% believe that this is just hype. Suppose a marketing study consists of a random sample of eight people who are given a sales talk about a new, improved product. What is the standard deviation of the number of people who believe that the product is in fact improved? What is the mean of the number of people who believe that the product is in fact improved?
Insurance Company A claims that its customers pay less for car insurance, on average than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 11 people who buy insurance from Company A, the mean cost is $⁢150 per month with a standard deviation of $⁢14. For 14 randomly selected customers of Company B, you find that they pay a mean of $⁢158 per month with a standard deviation of $⁢12. Assume that both populations are approximately normal and that the population variances are equal to test Company A’s claim at the 0.10 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.
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The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually (The Wall Street Journal, March 5, 2008). The average cost per person for crashes in the Tampa, Florida, area was reported to be $1613. Suppose this average cost was based on a sample of 55 persons who had been involved in car crashes and that the population standard deviation is σ = 600. What would you recommend if the study required a margin of error of $150 or less?
The major that you choose in college can have an impact on your future in terms of income and quality of life. Some majors, such as petroleum engineering and pharmaceutical sciences, make more on average than other majors. A random sample of 22 petroleum engineering and pharmaceutical sciences graduates have a mean annual salary of $54,118 with a standard deviation of $1479. Given that the distribution is approximately normal, test the hypothesis that the mean annual salary for petroleum engineering and pharmaceutical sciences graduates is $53,000. What is the critical value(s) for this test? The major that you choose in college can have an impact on your future in terms of income and quality of life. Some majors, such as petroleum engineering and pharmaceutical sciences, make more on average than other majors. A random sample of 22 petroleum engineering and pharmaceutical sciences graduates have a mean annual salary of $54,118 with a standard deviation of $1479. Given that the…
In its 2016 Auto Reliability Survey, Consumer Reports asked subscribers to report their maintenance and repair costs. Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $170 and a sample of 25 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles. Let 4 year old automobiles be represented by population 1. Ho : o - Select your answer - Ha : o? - Select your answer - b. At a 0.01 level of significance, what is your conclusion? Calculate the value of the test statistic (to 2 decimals). The…
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A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be ?¯=$14.50 . Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is ?=$3.50 . To address the CEO’s conjecture, the marketing manager carried out a hypothesis test of ?0:?=13.50 vs. ??:?>13.50 and obtained a ?‑value = 0.77. The marketing chooses a significance level of ?=0.10. If he uses this significance level throughout his work, how often will he reject a true null hypothesis? Group of answer choices a.He will reject 10% of all true null hypotheses. b. He will reject 1% of all true null hypotheses. c. He will reject 5% of all true null hypotheses. d. He will not reject 10% of all true null…
Insurance Company A claims that its customers pay less for car insurance, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 13 people who buy insurance from Company A, the mean cost is $150 per month with a standard deviation of $19. For 9 randomly selected customers of Company B, you find that they pay a mean of $157 per month with a standard deviation of $16. Assume that both populations are approximately normal and that the population variances are equal to test Company A's claim at the 0.05 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Ho: M₁ = μ₂ Ha:M₁ •H₂
A sample of 76 female workers and another sample of 48 male workers from a state produced mean weekly earnings of $743.50 for the females and $777.63 for the males. Suppose that the population standard deviations of the weekly earnings are $80.05 for the females and $88.68 for the males. The null hypothesis is that the mean weekly earnings are the same for females and males, while the alternative hypothesis is that the mean weekly earnings for females is less than the mean weekly earnings for males. Directions: • Label your answers with the correct statistical symbols. • If you use the Ti, identify which function and values you used to calculate. If you solve by hand, show all steps 2.5 The significance level for the test is 1%. What is/are the critical value(s)? 2.6. What is the value of the test statistic, rounded to three decimal places? 2.7. What is the p-value for this test, rounded to four decimal places? 2. 8. Using the p-value approach, do you reject or fail to reject the null…

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