The price of a pound of tomatoes varies seasonally. Michael King, a store manage
ID: 3350972 • Letter: T
Question
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
Info-
A) margin of error =
= 2.576 * 0.3/sqrt(39)
= 0.12374 < 0.2
hence
yes
99% confidence interval
One-Sample Z: C1
The assumed standard deviation = 0.3
(B) Variable N Mean StDev SE Mean 99% CI
C1 39 1.4554 0.3100 0.0480 (1.3316, 1.5791)
95% confidence interval
One-Sample Z: C1
The assumed standard deviation = 0.3
(C) Variable N Mean StDev SE Mean 95% CI
C1 39 1.4554 0.3100 0.0480 (1.3612, 1.5495)
90% confidence interval
One-Sample Z: C1
The assumed standard deviation = 0.3
(D) Variable N Mean StDev SE Mean 95% CI
C1 39 1.4554 0.3100 0.0480 (1.3612, 1.5495)
Question-
1. 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.
2. 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.
3. 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?
Explanation / Answer
1) AS confidence level increases, range is getting wider
this makes sense as confidence level increases , z increases , hence margin of error increases making confidence interval wider
2)
90 % confidence interval is more precise as its margin of error is smallest
3)
we can increase sample size to improve the precision of this confidence interval
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