A magazine uses a survey of readers to obtain customer satisfaction ratings for the nation's largest retailers. Each survey respondent is asked to rate a specified retailer in terms of six factors: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all six factors. Sample data representative of independent samples of Retailer A and Retailer B customers are shown below.

Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let μ₁ = population mean satisfaction score for Retailer A customers and μ₂ = population mean satisfaction score for Retailer B customers.)

(b) Assume that experience with the satisfaction rating scale of the magazine indicates that a population standard deviation of 11 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Find the value of the test statistic. (Round your answer to two decimal places.) =

Find the p-value. (Round your answer to four decimal places.)

p-value = .

(c)

Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Round your answers to two decimal places.)

_______ to ______

Which retailer, if either, appears to have the greater customer satisfaction?

According to a​ magazine, people read an average of more than two books in a month. A survey of 20 random individuals found that the mean number of books they read was 1.8 with a standard deviation of 1.28.

a. To test the​ magazine's claim, what should the appropriate hypotheses​ be?

b. Compute the test statistic.

c. Using a level of significance of​ 0.05, what is the critical​ value?

d. Find the​ p-value for the test.

e. What is your​ conclusion?

a. To test the​ magazine's claim, what should the appropriate hypotheses​ be?

Determine the null​ hypothesis, H0​, and the alternative​ hypothesis, H1.

H0​:

H1:

b. Compute the test statistic.____

c. Using a level of significance of​ 0.05, what is the critical​ value?_____

d. Find the​ p-value for the test.

e. What is your​ conclusion?

The​ p-value is _____ the chosen value of α​, so____ the null hypothesis. There is ____ evidence to conclude that mean is greater than 2.

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 40 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 40 weeks and that the population standard deviation is 3.2 weeks. Suppose you would like to select a random sample of 79 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 40.6. P(X > 40.6) = (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n = 79 n = 79 is randomly selected with a mean greater than 40.6. P(M > 40.6) =

(Enter your answers as numbers accurate to 4 decimal places.)

An article in Parenting magazine reported that 35% of Americans needed a vacation after visiting their families for the holidays. Suppose this is the true proportion of Americans who feel this way. A random sample of 200 Americans is taken. Let X be the number of people who feel that way in this random sample.

a) What is the mean of X?

b) Using the normal approximation, what is the probability that more than 80 people in the sample feel that they need a vacation after visiting their families for the holidays? (Round to 4 decimal places.)

A magazine published data on the best small firms in a certain year. These were firms that had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the corporate CEOs for a random sample of these firms. 47 58 52 62 56 59 74 63 53 50 59 60 60 57 46 55 63 57 47 55 57 43 61 62 49 67 67 55 55 49 Use this sample data to construct a 90% confidence interval for the mean age of CEO's for these top small firms. Use the Student's t-distribution. (Round your answers to two decimal places.)

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 39 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 39 weeks and that the population standard deviation is 3.5 weeks. Suppose you would like to select a random sample of 88 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is greater than 39.6. P(X > 39.6) =

(Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a sample of size n = 88 n=88 is randomly selected with a mean greater than 39.6. P(M > 39.6) =

(Enter your answers as numbers accurate to 4 decimal places.)

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 27 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 27 weeks and that the population standard deviation is 9 weeks. Suppose you would like to select a random sample of 32 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is less than 28. P(X < 28) =

Find the probability that a sample of size n = 32 is randomly selected with a mean less than 28. P(M < 28) =

Enter your answers as numbers accurate to 4 decimal places.

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 36.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36.3 weeks and that the population standard deviation is 7.5 weeks. Suppose you would like to select a random sample of 124 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 35.8 and 36.1.
P(35.8 < X < 36.1) =

Find the probability that a sample of size n=124 is randomly selected with a mean between 35.8 and 36.1.
P(35.8 < M < 36.1) =

A magazine article states the average age of women getting married for the first time is 25 years old. A researcher suspects this article may be incorrect. The researcher randomly selects 105 women who were recently married and found their average age was 24.7 years. The standard deviation of the population is 5.3 years. Perform a hypothesis test using ∝ = 0.10.

Step #2: Find the test value

Which test is needed? two, right, or left tailed test

Find the p-value.

do not reject or reject the null hypothesis?

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 36.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36.3 weeks and that the population standard deviation is 7.5 weeks. Suppose you would like to select a random sample of 124 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 35.8 and 36.1. P(35.8 < X < 36.1) =

Find the probability that a sample of size n=124 is randomly selected with a mean between 35.8 and 36.1. P(35.8 < M < 36.1) =

Enter your answers as numbers accurate to 4 decimal places.