The National Quality Research Center at the University of Michigan provides a quar-terly measure of consumer opinions about products and services (The Wall Street Journal,February 18, 2003). A survey of 10 restaurants in the Fast Food/Pizza group showed asample mean customer satisfaction index of 71. Past data indicate that the population stan-dard deviation of the index has been relatively stable with a = 5.a. What assumption should the researcher be willing to make if a margin of error is desired?b. Using 95% confidence, what is the margin of error?c. What is the margin of error if 99% confidence is desired?

Given Data : Sample Size, n = 10 Sample Mean, x̄ = 71 standard…

Answered: The National Quality Research Center at…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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.A study of 100 patients with back pain reported that the mean duration of pain was 12 months. It is known that the standard deviation of duration of back pain is 6.8 months. Assuming that the duration of this problem is normally distributed in the population; determine a 95% confidence interval for the mean duration of back pain in the population.
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?
You may need to use the appropriate technology to answer this question. The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state Pennsylvania showed a mean annual premium of $1,425 with a standard deviation of s = $160. (a) Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium. Ho: HS 1,503 H: µ > 1,503 Ho:H > 1,503 H: µ< 1,503 H0: μ2 1,503 H3: H< 1,503 Ho:H< 1,503 H.: μ2 1,503 Ho: H = 1,503 H: µ # 1,503 (b) What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.) (c) At a…
A polling organization reported data from a survey of 2000 randomly selected Canadians who carry debit cards. Participants in this survey were asked what they considered the minimum purchase amount for which it would be acceptable to use a debit card. Suppose that the sample mean and standard deviation were $9.14 and $7.70, respectively. (These values are consistent with a histogram of the sample data that appears in the report.)Do these data provide convincing evidence that the mean minimum purchase amount for which Canadians consider the use of a debit card to be appropriate is less than $10? Carry out a hypothesis test with a significance level of 0.01. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t = P-value = State your conclusion. Reject H0. We do not have convincing evidence that the mean minimum purchase amount for which Canadians consider it…
The National Coalition on Healthcare suggests that the mean annual premium that a health insurer charges an employer for a health plan covering a family of four averaged $13,000 in 2009. A sample of 30 families of four yields a mean annual premium paid by their employer to be $13,500 with a sample standard deviation of $300. We are interested in whether the mean annual premium that a health insurer charges an employer for a health plan covering a family of four is different from $13,000 using a significance level of 0.10. Select one: a. tdata = 9.129, do not reject Ho. b. tdata = 9.129, reject Ho. c. tdata = -9.129, do not reject Ho. O d. tdata = 4.156, reject Ho.
An economist would like to estimate the mean amount of money that a family spends towithin $35. If the amount spent by a family is considered to be normally distributed withstandard deviation $261, what sample size would be necessary to be 91% confident?
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitudes toward school. The survey yields several scores, one of which measures student attitudes toward studying. The mean student attitude score for college students is about 30, and standard deviation is about 12. A researcher in the Philippines is concerned about the declining performance of college graduates on professional licensure and board exams. She suspects that poor attitudes of students are partly responsible for the decline and that the mean for college seniors who plan to take professional licensure or board exams is less than 30. She gives the SSHA to an SRS of 144 college seniors in the Philippines who plan to take professional licensure or board exams. Suppose we know that the student attitude scores in the population of such students are Normally distributed with standard deviation σ = 12. (a) We seek evidence against the claim that μ = 30. What is the…
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A scientist has just been funded by the National Institutes of Health to conduct a very expensive study. As it happens, the budget has been cut. Therefore, the choice of laboratory for analysis of sample data is being re-visited. Suppose the choice is between laboratory “A” and “B”. Laboratory “A” has a standard deviation of one milligram and each sample analysis costs $3. Laboratory “B” has a standard deviation of two milligrams but each sample analysis costs $1. All other things being equal, is the principal investigator better off spending $9 on laboratory “A” or spending $9 on laboratory “B”?
In one city, the average amount of time that tenth-graders spend watching television each week is 23 hours. The principal of Birchwood High School believes it is less for the 10th grade students that at his school. For a sample of 95 tenth-graders from the school, the mean amount of time spent watching television per week was 21.9 hours. Assuming a population standard deviation of 3.1 hours, does the data provide sufficient evidence to conclude that for all tenth-graders at Birchwood High school, the mean amount of time spent watching television per week is less than the city average of 23 hours? Perform the appropriate hypothesis test using a significance level of 0.005. What are the hypotheses? What is the test statistic? Is it a z or a t? Find the P-value for this test statistic. How does it compare to the significance level? On the normal curve, indicate the location of the test statistic and the p-value. (label them on the graph) Write…

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