The price of a pound of tomatoes varies seasonally. Michael King, a store manager for a Kroger store in Detroit metro area, wants to price a pound of tomato competitively. He wants to use the price range for a pound of tomatoes in the Detroit metro area to price a pound of tomatoes for his store that he manages. He selects at random 39 stores in Detroit metro area and records the prices charged as shown below.

$1.32

$1.45

$1.20

$1.10

$0.99

$1.65

$1.99

$1.18

$1.59

$1.68

$1.43

$1.00

$1.29

$1.82

$1.09

$2.09

$1.79

$1.09

$1.72

$1.45

$1.53

$1.67

$1.78

$1.44

$1.60

$1.12

$1.39

$1.45

$1.78

$1.11

$1.18

$2.00

$1.00

$0.99

$1.45

$1.62

$1.45

$1.39

$1.89

Questions:

1. Is the sample size of 39 adequate using confidence level of 99% to estimate the price of a pound of tomatoes so that the estimated cost is within $0.20 of cost charged by the stores in Detroit Metro area? Assume that the population standard deviation is $0.30. Justify your answer based minimum sample size equation/calculation.
2. What is the 99% confidence interval range for price of a pound of tomatoes if the sample data above is used?
3. What is the 95% confidence interval range for price of a pound of tomatoes if the sample data above is used?
4. What is the 90% confidence interval range for price of a pound of tomatoes if the sample data above is used?
5. Review the results from part b, c, and d and explain what happens to the range of the intervals? Answer this question in context of whether the range is getting wider or narrower as the confidence level is changed. Do the results make sense? Explain why, or why not.
6. Describe what is precision. Next, comment on precision of the confidence intervals computed in part b, c, and d. Answer this question with respect to which of the three confidence intervals computed in part b, c, and d has a higher precision and why.
7. Based on the confidence interval computed in part b, if the decision maker wants to maintain the same confidence level, i.e. 99%, however, it is desired to improve the precision of this confidence interval, what option the decision maker has to improve the precision and still maintain the same confidence level?