Question

A study is done to estimate the true mean satisfaction rating for all customers of a particular retail store. A random sample of 200 customers is selected and a 99% confidence interval for the true mean satisfaction rating is 7.8 to 8.4 where 1 represents very dissatisfied and 10 represents completely satisfied. Based upon this interval, what conclusion should be made about the hypotheses: H0: μ = 8 versus Ha: μ ≠ 8 where μ = true mean satisfaction rating for all customers of this store at a = 0.01?

Answer 1

Explanation:

Based on the given information, the 99% confidence interval for the true mean satisfaction rating is 7.8 to 8.4. This means that we are 99% confident that the true mean satisfaction rating falls within this interval.

The null hypothesis (H0) states that the true mean satisfaction rating (μ) is equal to 8, while the alternative hypothesis (Ha) states that μ is not equal to 8.

Since the confidence interval does not include the value 8 (the null hypothesis), we can conclude that there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

In other words, based on the given interval, we have evidence to suggest that the true mean satisfaction rating for all customers of this retail store is different from 8.