Respuesta :
Answer:
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (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 [tex]\mu[/tex] 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".
[tex]\bar X=63.45[/tex] represent the sample mean
[tex]\mu[/tex] 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:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (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 [tex]\mu[/tex] at some level of confidence, and for this reason we can't asociate this to a chance or a probability.
