A basketball scout randomly selected 144 players and timed how long each player took to perform a certain drill. The times in this sample were distributed with a mean of 8 minutes. The population standard deviation was known to be 3 minutes.

A. find the critical value for a 95% confidence interval for the population mean of drill times.

B. Using 95% confidence interval, estimate the population mean of drill time.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability ([1-.95]/2 = .05/2 = .025) and its Z score.

A. 95% = mean ± 1.96 SEm

SEm = SD/√n

To find the critical value for a 95% confidence interval, you need to use the Z-table or a Z-score calculator. The critical value corresponds to the level of confidence and can be determined by finding the z-score that corresponds to the desired confidence level.

A. A 95% confidence interval corresponds to a significance level of 0.05 (one tail). Since the sample size is larger than 30 and the population standard deviation is known, we can use a z-distribution. For a 95% confidence interval, the critical value corresponds to a z-score of approximately 1.96.

B. To estimate the population mean of drill time using a 95% confidence interval, you can use the formula:

Confidence Interval = X̄ ± (Z * σ/√n)

Where:
- X̄ is the sample mean
- Z is the critical value at the desired confidence level (1.96 for a 95% confidence interval)
- σ is the population standard deviation
- n is the sample size

In this case, the sample mean (X̄) is not given, so we cannot calculate the confidence interval directly. However, since it is mentioned that the sample mean and the population mean are equal (both 8 minutes), we can use this value to estimate the population mean.

Using the formula above, the confidence interval would be:

Confidence Interval = 8 ± (1.96 * 3/√144)

Simplifying the equation:

Confidence Interval = 8 ± (1.96 * 3/12)

Confidence Interval = 8 ± 0.49

Therefore, the estimated population mean of drill time at a 95% confidence level is between 7.51 and 8.49 minutes.