Question

you are given a sample mean and the population standard deviation. use the information to construct the 90% and 95% confidence intervals for the population mean. interpret the results and compare the widths of the confidence intervals. from a random sample of 34 days. mean closing price of a certain stock was 121.96. standard deviation is 10.74.

Answer 1

Solution :

The 90% confidence interval for population mean is given as follows :

Where, x̄ is sample mean, σ is population standard deviation, n is sample size and Z(0.10/2) is critical z-value to construct 90% confidence interval.

We have,  x̄ = 121.96, σ = 10.74 and n = 34

Using Z-table we get, Z(0.10/2) = 1.645

Hence, 90% confidence interval for the population mean is,

The 90% confidence interval for population mean is (118.93, 124.99).

Interpretation : We are 90% confident that the true value of population mean closing price of the stock lies between 118.93 and 124.99.

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

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

We have,  x̄ = 121.96, σ = 10.74 and n = 34

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

Hence, 95% confidence interval for the population mean is,

The 95% confidence interval for population mean is (118.35, 125.57).

Interpretation : We are 95% confident that the true value of population mean closing price of the stock lies between 118.35 and 125.57.

Comparison of width : From the above two confidence intervals it is clear that width of 95% confidence interval for population mean is larger than the width of 90% confidence interval for population mean.

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