Question

The sample mean is 19.0, the sample standard deviation is 6.6, and n = 41. Establish a 90% confidence interval for the population mean. (by default two tailed test, α is reliability factor)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 19.0

Population standard deviation =    = 6.6

Sample size = n =41

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 * ( 6.6 /   41)

= 1.6956

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

- E < < + E

19.0 - 1.6956 <   < 19.0 + 1.6956

17.3044 <   < 20.6956

( 17.3044 ,  20.6956)