Question

Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of males from a certain country. Forty-five males are surveyed from a particular country. The sample mean is 71 inches. The sample standard deviation is 2.3 inches.
a). Construct a 95% confidence interval for the population mean height of males of this country.

Answer 1

Answer:

The 95% confidence interval for the population mean height of males of this country is between 67.136 inches and 74.864 inches.

Step-by-step explanation:

For the country, we only have the standard deviation of the sample, so we use the t distribution to build the confidence interval.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 45 - 1 = 44

Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of 0.95($t_{95}$). So we have T = 1.68

The margin of error is:

M = T*s = 1.68*2.3 = 3.864

In which s is the standard deviation of the sample. So

The lower end of the interval is the sample mean subtracted by M. So it is 71 - 3.864 = 67.136 inches

The upper end of the interval is the sample mean added to M. So it is 71 + 3.864 = 74.864 inches

The 95% confidence interval for the population mean height of males of this country is between 67.136 inches and 74.864 inches.