Question

In: Statistics and Probability

Based on a simple random sample of 35 adult males in North America, it is found...

Based on a simple random sample of 35 adult males in North America, it is found that the sample average height is 171cm with a sample standard deviation of 6cm. Construct 95% confidence interval for the mean height of all adult males in North America.

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Expert Solution

solution

Given that,

= 171

s =6

n = 35

Degrees of freedom = df = n - 1 = 35- 1 =34

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,34 = 2.032    ( using student t table)

Margin of error = E = t/2,df * (s /n)

=2.032 * (6 / 35) = 2.0608

The 95% confidence interval estimate of the population mean is,

- E < < + E

171 - 2.0608 < < 171+ 2.0608

168.9392 < < 173.0608

(168.9392 ,173.0608 )


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