Question

Question

Runners is a well established company with thousands of employees and they want to estimate the average age of their workers. A sample of 10 employees was taken. Assuming the population has a standard deviation of 8, we want to find a 90% confidence interval for the population mean.

If the mean of the sample is 31.5, what is the confidence interval estimate?

A population standard deviation is estimated te be 11 . we want to estimate the population mean within 0.5 with 90 percent of level of confidence . what sample size is required ?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 31.5

sample standard deviation = s = 8

sample size = n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

t/2,df = 1.833

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

= 1.833 * ( 8 / 10)

Margin of error = E = 4.64

The 90% confidence interval estimate of the population mean is,

  ± E

31.5 ± 4.64

(26.86 , 36.14)

Given that,

Population standard deviation = = 11

Margin of error = E = 0.5

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

  sample size = n = [Z/2* / E] 2

n = [1.645 * 11 / 0.5]2

n = 1309.72

Sample size = n = 1310