Question

I want to know how long basketball shoes last for people on average (as opposed to professional basketball players that go through them like I go through coffee). I rubbed a dusty coffee pot and a genie popped out to tell me that the standard deviation for the lifespan of all basketball shoes is 4 months. I polled 625 people at the PEIF on how long their shoes lasted, and I got an average of 20 months. (a) What is the 68% confidence interval for the population mean lifespan of a basketball shoe?

Answer 1

The 68% confidence interval for the population mean lifespan of basketball shoes is from 19.84 to 20.16 months.

Step-by-step explanation:

The student is asking for a 68% confidence interval for the population mean lifespan of basketball shoes, given a sample mean of 20 months, a standard deviation of 4 months, and a sample size of 625 people. The formula to calculate the 68% confidence interval (which is equivalent to one standard deviation in a normal distribution) is:

CI = ± Z * (σ / √ n)

Where CI is the confidence interval, Z is the Z-score corresponding to the confidence level, σ is the standard deviation, and n is the sample size. Since 68% confidence corresponds to a Z-score of 1 (because 68% of data falls within 1 standard deviation of the mean in a normal distribution), the calculation is as follows:

CI = ± 1 * (4 / √ 625)

CI = ± 1 * (4 / 25)

CI = ± 0.16

Therefore, the 68% confidence interval for the population mean lifespan of a basketball shoe is 20 ± 0.16 months, or from 19.84 to 20.16 months.