Question

Suppose a random sample of size 64 is selected from a population. The sample yields a mean of 26 and a standard deviation of 4. From this information, the 90% confidence interval to estimate the population mean can be computed to be _______.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 26

Population standard deviation =    = 4

Sample size = n =64

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 * ( 4 /  64 )

= 0.8225
At 90% confidence interval estimate of the population mean
is,

- E < < + E

26 - 0.8225 <   < 26 + 0.8225

25.1775 <   < 26.8225