A consumer product testing organization uses a survey of readers to obtain customer satisfaction ratings for the nation's largest supermarkets. Each survey respondent is asked to rate a specified supermarket based on a variety of factors such as: 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 factors. Suppose sample data representative of independent samples of two supermarkets' customers are shown below. Supermarket 1 Supermarket 2 n1 = 290 n2 = 300 x1 = 82 x2 = 81 (a) 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 ?1 = the population mean satisfaction score for Supermarket 1's customers, and let ?2 = the population mean satisfaction score for Supermarket 2's customers. Enter != for ≠ as needed.) H0: Ha: (b) Assume that experience with the satisfaction rating scale indicates that a population standard deviation of 16 is a reasonable assumption for both retailers. Conduct the hypothesis test. Calculate the test statistic. (Use ?1 − ?2. Round your answer to two decimal places.) Report the p-value. (Round your answer to four decimal places.) p-value = At a 0.05 level of significance what is your conclusion? Do not reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. Do not reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. (c) Which retailer, if either, appears to have the greater customer satisfaction? Supermarket 1Supermarket 2 neither Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Use x1 − x2. Round your answers to two decimal places.) to

A consumer product testing organization uses a survey of readers to obtain customer satisfaction ratings for the nation's largest supermarkets. Each survey respondent is asked to rate a specified supermarket based on a variety of factors such as: 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 factors. Suppose sample data representative of independent samples of two supermarkets' customers are shown below. Supermarket 1 Supermarket 2 n1 = 290 n2 = 300 x1 = 82 x2 = 81 (a) 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 ?1 = the population mean satisfaction score for Supermarket 1's customers, and let ?2 = the population mean satisfaction score for Supermarket 2's customers. Enter != for ≠ as needed.) H0: Ha: (b) Assume that experience with the satisfaction rating scale indicates that a population standard deviation of 16 is a reasonable assumption for both retailers. Conduct the hypothesis test. Calculate the test statistic. (Use ?1 − ?2. Round your answer to two decimal places.) Report the p-value. (Round your answer to four decimal places.) p-value = At a 0.05 level of significance what is your conclusion? Do not reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. Do not reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. (c) Which retailer, if either, appears to have the greater customer satisfaction? Supermarket 1Supermarket 2 neither Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Use x1 − x2. Round your answers to two decimal places.) to

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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You may need to use the appropriate appendix table or technology to answer this question.

Supermarket 1	Supermarket 2
n₁ = 290	n₂ = 300
x₁ = 82	x₂ = 81

(a)

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 ?₁ = the population mean satisfaction score for Supermarket 1's customers, and let ?₂ = the population mean satisfaction score for Supermarket 2's customers. Enter != for ≠ as needed.)

H₀:

H_a:

(b)

Assume that experience with the satisfaction rating scale indicates that a population standard deviation of 16 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Calculate the test statistic. (Use

?₁ − ?₂.

Round your answer to two decimal places.)

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

p-value =

At a 0.05 level of significance what is your conclusion?

Do not reject H₀. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H₀. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. Do not reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H₀. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.

(c)

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

Supermarket 1Supermarket 2 neither

Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Use

x₁ − x₂.

Round your answers to two decimal places.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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