Question

A simple random sample of 60 items resulted in a sample mean of 90. The population standard deviation is σ = 17.

a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places

Answer 1

Solution :

a) The 95% confidence interval for population mean is given as follows:

Where, x̄ is sample mean, σ is population standard deviation and Z(0.05/2) is critical z-value to construct 95% confidence interval.

We have, x̄ = 90,  σ = 17 and n = 60

Using Z-table we get, Z(0.05/2) = 1.96

Hence, 95% confidence interval for population mean is,

The 95% confidence interval for population mean is,

(85.7, 94.3)

b) The 95% confidence interval for population mean is given as follows:

Where, x̄ is sample mean, σ is population standard deviation and Z(0.05/2) is critical z-value to construct 95% confidence interval.

We have, x̄ = 90,  σ = 17 and n = 120

Using Z-table we get, Z(0.05/2) = 1.96

Hence, 95% confidence interval for population mean is,

The 95% confidence interval for population mean is,

(86.96, 93.04)

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