According to the South Dakota Department of Health, the mean number of hours of

Question

According to the South Dakota Department of Health, the mean number of hours of TV viewing per week is higher among adult women than men. A recent study showed women spent an average of 30 hours per week watching tv and men 25 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 4.0 hours and is 4.4 hours for the men. what percent of women watch less than 35 hours a week what percent of men watch more than 20 hours a week round z score and final answer two decimal places and plz show work, i am trying to learn! (:

Explanation / Answer

Ans.

a) Percent of women watch TV less than 35 hours a week

Given that expectation of mean or sample mean of women spend time in watching TV = 30 hours

population mean = 35 hours

Standard deviation = 4.0 hours

The area under normal curve is to left that means alternative hypothsis is where population mean is less than 35 .

Z score = population mean - expectation of mean / standard deviation

Z score = 35 - 30 / 4.0 = 1.25

The area under the standard normal curve to the left of Z = 1.25 is .8944 or 89.44% ( see z statistic table )

Thus 89.44 % of women watch less than 35 hours a TV per week.

b) percent of men watch more than 20 hours a week

exectation of mean men spending time to watch TV per week or sample mean = 25 hours

population mean = 20 hours

standard deviation for men = 4.4 hours

z score = population mean - expectation of mean / standard deviation = 20 - 25 / 4.4 = -1.13

The area under standard normal curve to right of Z = -1.13

In z statistic table values of area under normal curve are provided only for left of z. In this part we need to find for right of Z score since alternative hyothesis is set as where population mean is more than 20 .

To find for right of Z first see in Z statistic table of negative value ones. Where value of -1.13 is .1292 or 12.92%. Now right of Z is found by subtracting it from 1. thus area to right of Z is = 1 - .1292 = 0.8708 or 87.08%.

So, 87.08% of men watch more TV than 20 hours a week.

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