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 196 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? (b) What is the 99.7% confidence interval for the population mean lifespan of a basketball shoe? (c) Draw appropriately shaded bell curves to show the difference between these. You will show all of this work on your paper to be submitted later. Enter "True" here in EduCat. Select one: True False

Answer 1

The 68% confidence interval for the lifespan of basketball shoes is 19.714 to 20.286 months, and the 99.7% confidence interval is 19.142 to 20.858 months. These results were calculated using the provided standard deviation and sample mean with a given sample size.

Step-by-step explanation:

The question revolves around finding the confidence intervals for the population mean lifespan of basketball shoes, based on a sample. With a standard deviation (σ) of 4 months and a sample mean (μ) of 20 months from a sample size (n) of 196, we can calculate the confidence intervals.

(a) The 68% confidence interval is found by using the 1 standard deviation from the mean in a normal distribution, which in this case would be μ +/- 1σ/√n. Hence, the 68% confidence interval is 20 +/- (4/√196), which simplifies to 20 +/- 0.286. Therefore, the interval is 19.714 to 20.286 months.

(b) For the 99.7% confidence interval, we use 3 standard deviations from the mean, which gives us 20 +/- 3(4/√196), simplifying to 20 +/- 0.858. Thus, the interval is 19.142 to 20.858 months.

The student is requested to draw bell curves for visual representation and analyse the differences between the two confidence intervals, which will be done on paper.