Question

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 = 280	n2 = 300
x1 = 89	x2 = 88

(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 μ₁ = the population mean satisfaction score for Supermarket 1's customers, and let μ₂ = 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 13 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Calculate the test statistic. (Use

μ₁ − μ₂.

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?

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

Answer 1

(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 μ1 = the population mean satisfaction score for Supermarket 1's customers, and let μ2 = the population mean satisfaction score for Supermarket 2's customers. Enter != for ≠ as needed.)

Ho : =

Ha:  != ()

(b)

Assume that experience with the satisfaction rating scale indicates that a population standard deviation of 13 is a reasonable assumption for both retailers. Conduct the hypothesis test.

Calculate the test statistic. (Use - )

n1= 280 = 89

n2 = 300   = 88

Test Statistic : 0.93

For Two tailed test :

p-value = 0.3546

As P-Value i.e. is greater than Level of significance i.e (P-value:0.3546 > 0.05:Level of significance);

Do not Reject Null Hypothesis

At a 0.05 level of significance what is your conclusion?

Do not reject Ho. There is not 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?

neither

(as There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. )

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

Confidence interval for the difference between the population means

for 95% confidence interval = (100-95)/100 =0.05

/2 =0.05/2=0.025

Z/2 =Z0.025 = 1.96

95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers

95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers = (-1,12, 3.12)