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 = 270	n2 = 300
x1 = 84	x2 = 83

(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 17 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 not 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.    Do not 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.

(c)

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

Supermarket 1

Supermarket 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)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 ╪   0
.

b)

Level of Significance ,    α =    0.05          
                  
sample #1   ------->              
mean of sample 1,    x̅1=   84          
population std dev of sample 1,   σ1 =    17          
size of sample 1,    n1=   270          
                  
sample #2   --------->              
mean of sample 2,    x̅2=   83          
population std dev of sample 2,   σ2 =    17          
size of sample 2,    n2=   300          
                  
difference in sample means = x̅1 - x̅2 =    84   -   83   =   1
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    1.4261          
                  
Z-statistic = ((x̅1 - x̅2)-µd)/SE =    1   /   1.4261   =   0.70
                        
                   p-value =        0.2416   [excel function =NORMSDIST(z)]      

Desison:   p-value>α ,

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

.......

c)

neither ,appears to have the greater customer satisfaction

Level of Significance ,    α =    0.05          
z-critical value =    Z α/2 =    1.9600   [excel function =normsinv(α/2) ]      
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    1.4261          
margin of error, E = Z*SE =    1.9600   *   1.426   =   2.7951
                  
difference of means = x̅1 - x̅2 =    84   -   83   =   1.000
confidence interval is                   
Interval Lower Limit= (x̅1 - x̅2) - E =    1.000   -   2.795   =   -1.7951
Interval Upper Limit= (x̅1 - x̅2) + E =    1.000   +   2.795   =   3.7951
CI (-1.80 , 3.80)

............................

Please revert back in case of any doubt.

Please upvote. Thanks in advance.