Question

Undergraduate GPAs It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within 0.21 at the 95% confidence level? The population standard deviation is 1.24. If needed, round your final answer up to the next whole number

Answer 1

To estimate the mean GPA of each undergraduate class at a large university within a certain margin of error, you need to determine the required sample size. In this case, with a 95% confidence level, a population standard deviation of 1.24, and a desired margin of error of 0.21, the calculated sample size is 119.

Step-by-step explanation:

To estimate the mean GPA of each undergraduate class at the university within 0.21 at the 95% confidence level, you need to determine the required sample size. In this case, the population standard deviation is 1.24.

To calculate the sample size, you can use the formula:

Sample Size = ((Z-score * Standard Deviation) / Margin of Error)^2

Here, the Z-score for a 95% confidence level is approximately 1.96. Plugging in the given values, we get:

Sample Size = ((1.96 * 1.24) / 0.21)^2 = 118.2

Since the sample size must be a whole number, rounding up to the next whole number gives a required sample size of 119.