Question

Use the sample information x=44, a=6, n=17 to calculate the following confidence intervals for u assuming the sample is from a normal population

(a) 90% confidence interval is ? to ?

(b) 95% confidence interval is ? to ?

(c) 99% confidence interval is ? to ?

Answer 1

Solution :

Given that,

a) Z/2 = Z0.05 = 1.645

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

= 1.645 * ( 6 /  17 )

= 2.3938

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

- E < < + E

44 - 2.3938 <   < 44 + 2.3938

(41.6062 <   < 46.3938)

b) Z/2 = Z0.025 = 1.96

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

= 1.96 * ( 6 /  17 )

= 2.8522

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

- E < < + E

44 - 2.8522 <   < 44 + 2.8522

(41.1478 <   < 46.8522)

c) Z/2 = Z0.005 = 2.576

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

= 2.576 * ( 6 /  17 )

= 3.7486

At 99% confidence interval estimate of the population mean is,

- E < < + E

44 - 3.7486 <   < 44 + 3.7486

(40.2514 <   < 47.7486)