A T-shirt company is interested in knowing the average retail price charged for one product sold in stores across the country. The company cannot justify a national census to generate this information. Based on the company information system's list of all retailers who carry the product, a researcher for the company contacts 36 of these retailers and ascertains the retail prices for the product. A population standard deviation is known to be $1.13. The price data (in dollar) is listed in the following table.
|
22.3
|
21.6
|
21.2
|
20.1
|
19.9
|
22.3
|
|
21.1
|
23.1
|
20.7
|
18.7
|
21.0
|
21.2
|
|
19.8
|
21.7
|
21.8
|
20.9
|
20.8
|
22.0
|
|
23.0
|
21.8
|
22.2
|
20.5
|
21.7
|
21.4
|
|
22.9
|
23.2
|
21.5
|
21.0
|
18.2
|
21.9
|
|
20.2
|
21.9
|
22.6
|
22.4
|
21.7
|
21.6
|
(a) Use Excel to calculate the sample average retail price.
b) Set up a 90% confidence interval of the population average retail price charged for this T-shirt item.
c) Does the population of retail price have to be normally distributed here? Explain briefly.
d) What is the probability that the mean retail price, in a sample of size 36, is greater than $21? Assume the population average retail price is $21.4.