Question

1. Customer satisfaction data for two similar stores are provided below. The scores are averages of ratings on a scale of 1 to 10. Assume the populations are normally distributed.

Store A: sample size = 25, sample mean = 7.9, population standard deviation = 1.4

Store B: sample size = 27, sample mean = 8.6, population standard deviation = 1.9

Construct a 95% confidence interval for the difference between customer satisfaction for Stores A and B. State your conclusion in terms of the problem

Answer 1

a)

b)

Therefore, based on the data provided, the 95% confidence interval for the difference between the population means μ1​−μ2​ is -1.603<μ1​−μ2​<0.203, which indicates that we are 95% confident that the true difference between population means is contained by the interval (−1.603,0.203).

Since 0 is contained in the interval, at the 5% level of significance we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that the mean customer satisfaction is different for the two stores.

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