Question

Supermarket Customer Satisfaction. Consumer Reports uses a survey of readers to obtain customer satisfaction ratings for the nation’s largest supermarkets (Consumer Reports, https://www.consumerreports.org/products/grocery-stores-supermarkets/ratings-overview/). 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. Publix Trader Joe’s n₁ = 250 n₂ = 300 x₁ = 86 x₂ = 85 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. 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. At a .05 level of significance what is your conclusion? c. Which retailer, if either, appears to have the greater customer satisfaction? Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers.

Answer 1

Given that,
mean(x)=86
standard deviation , σ1 =12
number(n1)=250
y(mean)=85
standard deviation, σ2 =12
number(n2)=300
null, Ho: u1 = u2
alternate, H1: μ1 != u2
level of significance, alpha = 0.05
from standard normal table, two tailed z alpha/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=86-85/sqrt((144/250)+(144/300))
zo =0.97
| zo | =0.97
critical value
the value of |z alpha| at los 0.05% is 1.96
we got |zo | =0.973 & | z alpha | =1.96
make decision
hence value of | zo | < | z alpha | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 0.97 ) = 0.33049
hence value of p0.05 < 0.33049,here we do not reject Ho
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(a) null, Ho: u1 = u2 ; alternate, H1: μ1 != u2
(b) test statistic: 0.97
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.33049
there is no difference between the population mean customer satisfaction scores for the two retailers
(c)
CI = [ ( 86-85) ±Z a/2 * Sqrt( 144/250+144/300)]
= [ (1) ± Z a/2 * Sqrt( 1.056) ]
= [ (1) ± 1.96 * Sqrt( 1.056) ]
= [-1.0141 , 3.0141]