Question

A parking officer is conducting an analysis of the amount of time left on parking meters after a motorist left a parking space. A quick survey of 15 cars that have left their metered parking spaces produced the following times (in minutes). Estimate with 95% and 80% confidence the mean amount of time left for all the vacant meters.

1. Applying the correct Statistical Analysis. Show your results
2. Estimated mean?
3. Upper 95% Confidence limit.
4. Lower 95% Confidence limit
5. Which of the confidence limits is the widest?

Data Time:

22
15
1
14
0
9
17
31
18
26
23
15
33
28
20

Answer 1

Data(X) = 22, 15, 1, 14, 0, 9, 17, 31, 18, 26, 23, 15, 33, 28, 20

n=15

Estimated mean = = ( Xi)/n = 272 /15 = 18.13

Variance = {( X^2 ) - n* ^2 }/ (n-1) = 95.124

Standard deviation, S= 9.753

N ( )

N ( 0,1)

=S

t 14

= 9.753 / = 2.518

t/2=0.025,14 = 2.145

95% confidence interval for average act score is [ - t/2=0.025,14 * ,   + t/2=0.025,14 * ]

=[18.13 - 2.145* 2.518, 18.13 + 2.145* 2.518] = [ 12.729 , 23.531] [Ans]

t/2=0.1,14 = 1.345

80% confidence interval for average act score is [ - t/2=0.1,14 * ,   + t/2=0.1,14 * ]

=[18.13 - 1.345* 2.518, 18.13 + 1.345* 2.518] = [ 14.743 , 21.517] [Ans]

Upper 95% Confidence limit = 23.531

Lower 95% Confidence limit = 12.729

95% Confidence limit is wider.

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