Question

Explain why if a random sample of 50 provides a sample mean of 31 with a standard deviation of s=14. The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 31

sample standard deviation = s = 14

sample size = n = 50

Degrees of freedom = df = n - 1 = 50 - 1 =49

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90= 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,49 = 1.677

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

= 1.677 * (14 / 50)

= 3.32

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

+ E

31 + 3.32

34.32

The upper bound is 34.32