Question

A random sample of college basketball players had an average height of 63.45 inches. Based on this sample, (62.1, 64.8) found to be a 96% confidence interval for the population mean height of college basketball players. Select the correct answer to interpret this interval.a. We are 96% confident that the population mean height of college basketball palyers is 63.45 inches.b. A 96% of college basketball players have height between 62.1 and 64.8 inches.c. There is a 96% chance that the population mean height of college basketball players is between 62.1 and 64.8 inches.d. We are 96% confident that the population mean height of college basketball players is between 62.1 and 64.8 inches.

Answer 1

The confidence interval for the mean is given by the following formula:

`\bar X \pm t_(\alpha/2)(s)/(√(n))` (1)

And for this case the confidence interval is given by (62.1; 64.8)

Now we need to interpret this confidence interval and we can conclude this:

d. We are 96% confident that the population mean height of college basketball players is between 62.1 and 64.8 inches.

And the reason of this is because the principal interest when we create a confidence interval is in order to estimate the population mean
`\mu` at some level of confidence, and for this reason we can't asociate this to a chance or a probability.

Explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

`\bar X=63.45` represent the sample mean

`\mu` population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

`\bar X \pm t_(\alpha/2)(s)/(√(n))` (1)

And for this case the confidence interval is given by (62.1; 64.8)

Now we need to interpret this confidence interval and we can conclude this:

d. We are 96% confident that the population mean height of college basketball players is between 62.1 and 64.8 inches.

And the reason of this is because the principal interest when we create a confidence interval is in order to estimate the population mean
`\mu` at some level of confidence, and for this reason we can't asociate this to a chance or a probability.