Question

Valarie's husband Mark, an avid golfer, claims that his average drive is greater than 250 yards. To prove this, he measured 9 drives from a round of golf. Here are his distances, in yards:

262, 247, 255, 239, 275, 257, 260, 242, 248

Construct an 80% confidence interval for the mean length of all of Mark's drives.

How do you do this and what work do you show?

Answer 1

To construct an 80% confidence interval for the mean length of Mark's drives, calculate the sample mean and standard deviation, find the appropriate t-score, calculate the margin of error, and use these to find the upper and lower bounds of the interval.

Step-by-step explanation:

The student is asking how to construct an 80% confidence interval for the mean length of all of Mark's golf drives. To perform this calculation, you first need to calculate the sample mean and the sample standard deviation. Following that, you use the t-distribution, since the sample size is less than 30, to find the t-score that corresponds to the 80% confidence level. With the t-score, the sample mean, and the sample standard deviation, you then compute the margin of error and apply it to the sample mean to create the confidence interval.

Here is the step-by-step process:

1. Compute the sample mean (μ).
   
2. Compute the sample standard deviation (s).
3. Determine the degrees of freedom (df), which is n - 1 (where n is the sample size).
4. Find the t-score that corresponds to the 80% confidence level and the degrees of freedom using a t-distribution table or a calculator.
5. Calculate the margin of error (ME) using the formula ME = t * (s/√n).
6. Finally, construct the confidence interval using the sample mean and the margin of error, which is μ ± ME.

Note that you'll need the actual data of Mark's 9 golf drives to complete the calculations, which are not provided in the question.