At a particular academically challenging high school, the average gpa of a high school senior is known to be normally distributed. after a sample of 20 seniors is taken, the average gpa is found to be 2.71 and the variance is determined to be 0.25. find a 90% confidence interval for the population mean gpa.

Solution: The 90% confidence interval for the population mean is:

Where:

is the critical value at 0.1 significance level for df = n-1 =20-1=19

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

The 90% confidence interval for the population mean gpa is [2.526,2.894].

Step-by-step explanation:

The confidence interval for population mean is

Where, μ is population mean, σ is standard deviation, z* is the value of z-score and n is number of samples.

The z-score value for 90% confidence interval is 1.645.

The average gpa is found to be 2.71, so μ=2.71. The variance is 0.25, it means

The 90% confidence interval for population mean is

Therefore the 90% confidence interval for the population mean gpa is [2.526,2.894].

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