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:

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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:

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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. Sodf = 50 - 1 = 49Now, 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([tex]t_{99}[/tex]). So we have T = 2.68The margin of error is:M = T*s = 2.68*2.4 = 6.432.In which s is the standard deviation of teh sample. SoThe lower end of the interval is the sample mean subtracted by M. So it is 23.6 - 6.432 = 17.168 minutesThe upper end of the interval is the sample mean added to M. So it is 23.6 + 6.432 = 30.032 minutesThe 99% confidence interval for the mean time required by all individuals to compete the form is between 17.168 minutes and 30.032 minutes.

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