Question

Fifty randomly selected individuals were timed completing a tax form. The samplemean was 23.6 minutes; the sample standard deviation was 2.4 minutes. A 99% Con-fidence interval for the mean time required by all individuals to compete the form isabout:

Answer 1

Answer:

The 99% confidence interval for the mean time required by all individuals to compete the form is between 17.168 minutes and 30.032 minutes.

Step-by-step explanation:

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 = 50 - 1 = 49

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of 0.99($t_{99}$). So we have T = 2.68

The margin of error is:

M = T*s = 2.68*2.4 = 6.432.

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

The lower end of the interval is the sample mean subtracted by M. So it is 23.6 - 6.432 = 17.168 minutes

The upper end of the interval is the sample mean added to M. So it is 23.6 + 6.432 = 30.032 minutes

The 99% confidence interval for the mean time required by all individuals to compete the form is between 17.168 minutes and 30.032 minutes.