The freshness of produce at a super-store is rated on a scale of 1 to 5 with 5 being very fresh. From a random sample of 49 customers, the average score was 3.8 with a standard deviation of 0.7.   a) Obtain an 80% confidence interval for the population mean - the mean score for the distribution of all possible customers. Specify and check all conditions needed for the problem.   b) Does the interval obtained in Part(a) contain the population mean score for the customers? Why?   c) Does the interval obtained in Part(a) contain the sample mean score for the customers in the data? Why?

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The freshness of produce at a super-store is rated on a scale of 1 to 5 with 5 being very fresh. From
a random sample of 49 customers, the average score was 3.8 with a standard deviation of 0.7.
 
a) Obtain an 80% confidence interval for the population mean - the mean score for the
distribution of all possible customers. Specify and check all conditions needed for the
problem.
 
b) Does the interval obtained in Part(a) contain the population mean score for the customers?
Why?
 
c) Does the interval obtained in Part(a) contain the sample mean score for the customers in the
data? Why?
 
d.) In a long series of repeated experiments, with new random samples of 49 customers each
day, what proportion of the resulting confidence intervals will contain the true population
mean? Explain your reasoning.
 
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