Question

In: Statistics and Probability

PROBLEM 2 Situation The price of a pound of tomatoes varies seasonally. Michael King, a store...

PROBLEM 2

Situation

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

Action

 

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.
What is the 99% confidence interval range for price of a pound of tomatoes if the sample data above is used?
What is the 95% confidence interval range for price of a pound of tomatoes if the sample data above is used?
What is the 90% confidence interval range for price of a pound of tomatoes if the sample data above is used?

Solutions

Expert Solution

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


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


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


Variable   N    Mean   StDev SE Mean       95% CI
C1        39 1.4554 0.3100   0.0480 (1.3612, 1.5495)

orchestra answered 2 years ago
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