Question

The table below gives the average high temperatures in January and July for 12 random cities...

The table below gives the average high temperatures in January and July for 12 random cities in a region with 155 cities. Write a 99​% confidence interval for the mean temperature difference between summer and winter in the region. Mean High Temperatures ​(degrees​F)

City A B C D E F G H I J K L

July 77 70 76 73 88 89 71 86 75 67 74 82

Jan. 34 34 44 35 56 55 41 48 46 42 19 35

The confidence interval is

Math   Statistics-And-Probability   
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Answer #1

Confidence interval for difference between two population means of paired samples is given as below:

Confidence interval = Dbar ± t*SD/sqrt(n)

From given data, we have

Dbar = 36.58333333

Sd = 8.404093519

n = 12

df = n – 1 = 11

Confidence level = 99%

Critical t value = 3.1058

(by using t-table)

Confidence interval = Dbar ± t*SD/sqrt(n)

Confidence interval = 36.58333333 ± 3.1058*8.404093519/sqrt(12)

Confidence interval = 36.58333333 ± 7.5349

Lower limit = 36.58333333 - 7.5349 = 29.05

Upper limit = 36.58333333 + 7.5349 = 44.12

29.05 < µd < 44.12

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