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In: Statistics and Probability

A sample of 53 night-school students' ages is obtained in order to estimate the mean age...

A sample of 53 night-school students' ages is obtained in order to estimate the mean age of night-school students. x = 25.5 years. The population variance is 13.

(b) Find the 95% confidence interval for μ. (Give your answer correct to two decimal places.)

Lower Limit
Upper Limit


(c) Find the 99% confidence interval for μ. (Give your answer correct to two decimal places.)

Lower Limit
Upper Limit

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 25.5

Population standard deviation = = 3.6

Sample size = n = 53

a)

At 95% confidence level the z is ,

Z/2 = Z0.025 = 1.96

Margin of error = E = Z/2* ( /n)

= 1.96* (3.6 / 53 )

= 0.97

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

- E < < + E

25.5 - 0.97 < < 25.5 + 0.97

24.53 < < 26.47

Lower limit = 24.53

Upper limit = 26.47

b)

At 99% confidence level the z is ,

Z/2 = Z0.005 = 2.576

Margin of error = E = Z/2* ( /n)

= 2.576* (3.6 / 53 )

= 1.27

At 99% confidence interval estimate of the population mean is,

- E < < + E

25.5 - 1.27 < < 25.5 + 1.27

24.23 < < 26.77

Lower limit = 24.23

Upper limit = 26.77

orchestra answered 2 years ago
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