Question

Use the sample information x¯ = 38, σ = 4, n = 11 to calculate the following confidence intervals for μ assuming the sample is from a normal population

90% confidence interval is from

95% confidence interval is from  

99% confidence interval is from

Answer 1

Solution :

Given that,

Sample size = n = 11

Z_/2 = 1.645

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

= 1.645 * (4 / 11)

= 1.98

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

- E < < + E

38 - 1.98 < < 38 + 1.98

36.02 < < 39.98

90% confidence interval is from :(36.02 , 39.98)

Sample size = n = 11

Z_/2 = 1.96

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

= 1.96 * (4 / 11)

= 2.36

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

- E < < + E

38 - 2.36 < < 38 + 2.36

35.64 < < 40.36

95% confidence interval is from: (35.64 , 40.36)

Sample size = n = 11

Z_/2 = 2.576

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

= 2.576 * (4 / 11)

= 3.11

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

- E < < + E

38 - 3.11 < < 38 + 3.11

34.89 < < 41.11

99% confidence interval is from : (34.89 , 41.11)