Question

In: Statistics and Probability

Assuming the sample size is 30, the sample mean (X) is 24.75, the population standard deviation...

Assuming the sample size is 30, the sample mean (X) is 24.75, the population standard deviation (σ) is 5, a 95% confidence interval for the population mean would have lower bound of _________________ and upper bound of _______________________.

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 24.75

Population standard deviation = =5

Sample size n =30

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)
=1.96 * (5 / $\sqrt$ 30)

= 1.7892
At 95% confidence interval estimate of the population mean
is,

- E < < + E

24.75 - 1.7892< < 24.75 + 1.7892

22.9608 < < 26.5392
( lower bound= 22.9608 ,upper bound= 26.5392)

orchestra answered 2 years ago

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