**Hypothesis Testing of Customer Satisfaction Scores for Supermarkets**Consumer Reports utilizes a survey of readers to gather customer satisfaction ratings for major supermarkets across the nation. Each survey respondent rates a specified supermarket based on various factors such as product quality, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes these ratings, with 100 meaning complete satisfaction in all areas. Below is sample data from independent samples of Publix and Trader Joe’s customers.**Data:**- **Publix:** - Sample size (\(n_1\)): 250 - Mean satisfaction score (\(\bar{x}_1\)): 86- **Trader Joe’s:** - Sample size (\(n_2\)): 300 - Mean satisfaction score (\(\bar{x}_2\)): 85**Problem Statement:**a. **Formulation of Hypotheses:** - Null Hypothesis (\(H_0\)): \(\mu_1 - \mu_2 = 0\) - Alternative Hypothesis (\(H_a\)): \(\mu_1 - \mu_2 \neq 0\)b. **Hypothesis Testing:** - Assume a population standard deviation of 12. - Perform the hypothesis test and determine the p-value (to 3 decimal places). - With a significance level of 0.05, determine your conclusion: I. Reject \(H_0\). Insufficient evidence suggests the mean satisfaction scores differ for the two retailers. II. Do not reject \(H_0\). Insufficient evidence suggests the mean satisfaction scores differ for the two retailers. III. Reject \(H_0\). Sufficient evidence suggests the mean satisfaction scores differ for the two retailers. IV. Do not reject \(H_0\). Sufficient evidence suggests the mean satisfaction scores differ for the two retailers.c. **Comparison of Retailers:** - Determine which retailer, if any, has greater customer satisfaction. - Provide a 95% confidence interval for the difference in population mean customer satisfaction scores. Enter negative numbers if applicable, and express it to 2 decimal places.**Excel File:**- [Data file: data10-07.xlsx](data10-07.xlsx)

We have given sample data representative of independent samples of Publix and Trader Joe's customers, as shown below:, ,,Where, and are the sample means, and are the population standard deviations, and and are the sample sizes.a. The null and alternative hypotheses are written as follows:This is a two-tailed hypothesis.Because we have to test whether there is a difference between the population mean customer satisfaction scores for the two retailers.b. Given that the population standard deviation is known and assuming the data is approximately normally distributed, we can use a two-sample z-test.The test statistic is calculated as follows:So, the value of the test statistic is .The p-value of the two-tailed -test is obtained by using the Excel function: "=2*(1-NORM.S.DIST(0.9731, TRUE))".The p-value is .The level of significance: Decision rule: If the p-value of the test statistic is greater than the level of significance, then we do not reject the null hypothesis; otherwise, we reject the null hypothesis.Here, the calculated p-value is greater than the significance level . We do not reject the null hypothesis.Conclusion:Do not reject . There is not sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers.Option (II) is correct.c. The confidence interval for the difference between the population mean is given by:Significance level: Hence,The critical value of the two-tailed -test is obtained using the Excel function: "=ABS(NORM.S.INV(0.05/2))".Critical value: .The confidence interval for the difference between the population mean customer satisfaction scores is calculated as follows:So, the confidence interval for the difference between the population mean customer satisfaction scores is between to .a. The null and alternative hypotheses:b. The value of the test statistic is .The p-value is .Conclusion:Do not reject . There is not sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers.Option (II) is correct.c. The confidence interval for the difference between the population mean customer satisfaction scores is between to .

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Consumer Reports uses a survey of readers to obtain customer satisfaction ratings for the nation's largest supermarkets (Consumer Reports website). 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. Sample data representative of independent samples of Publix and Trader Joe's customers are shown below. Excel File: data10-07.xlsx Publix n₁ = 250 T1 = 86 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. Ho: 1-2 - Select your answer - H₂:1-12 Select your answer - + b. Assume that experience with the Consumer Reports satisfaction rating scale indicates that a population standard deviation of 12 is a reasonable assumption for both retailers. Conduct the hypothesis test and report the p-value. (to 3 decimals) + Trader Joe's n₂ = 300 T2 = 85 p-value = At a 0.05 level of significance what is your conclusion? I. Reject Ho. There is not sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers. I. Do not reject Ho. There is not sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers. I. Reject Ho. There is sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers. V. Do not reject Ho. There is sufficient evidence to conclude that the mean satisfaction scores differ for the two retailers. - Select your answer - to c. Which retailer, if either, appears to have the greater customer satisfaction? - Select your answer - Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. Enter negative values as negative numbers, if any. (to 2 decimals)