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.

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

  (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 at some level of confidence, and for this reason we can't asociate this to a chance or a probability.

Step-by-step 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".

represent the sample mean

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:

  (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 at some level of confidence, and for this reason we can't asociate this to a chance or a probability.