In general, high school and college students are the most pathologically sleep-d
ID: 2906576 • Letter: I
Question
In general, high school and college students are the most pathologically sleep-deprived segment of the population. Their alertness during the day is on par with that of untreated narcoleptics and those with untreated sleep apnea. Not surprisingly, teens are also 71 percent more likely to drive drowsy and/or fall asleep at the wheel compared to other age groups. (Males under the age of twenty-six are particularly at risk.) The accompanying data set represents the number of hours 25 college students at a small college in the northeastern United States slept and is from a random sample. Enter this data into C1 of Minitab Express. 6 7 6 7 6 7 7 7 8 6 6 6 8 8 8 5 4 6 7 8 5 8 7 6 7 For the analyses that follow, we shall use 90%, 95%, and 99% as the confidence levels for the confidence interval. 5% as the level of significance (?) for the hypothesis test. 7 hours sleep as the null hypothesis (according to The Sleep Foundation).
n. Write your CONCLUSION to this hypothesis test in context. See step 5 on page 498Explanation / Answer
Solution:
Here, we have to find the 90%, 95%, and 99% confidence intervals for the population means or average number of sleeping hours. Also, we have to test the hypothesis test at 5% level of significance. We have to solve this question by using Minitab. Required Minitab outputs for the confidence intervals and hypothesis tests are given as below:
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One-Sample T: Hours
Test of mu = 7 vs mu not = 7
Variable N Mean StDev SE Mean
Hours 25 6.640 1.075 0.215
Variable 90.0% CI T P
Hours ( 6.272, 7.008) -1.67 0.107
One-Sample T: Hours
Test of mu = 7 vs mu not = 7
Variable N Mean StDev SE Mean
Hours 25 6.640 1.075 0.215
Variable 95.0% CI T P
Hours ( 6.196, 7.084) -1.67 0.107
One-Sample T: Hours
Test of mu = 7 vs mu not = 7
Variable N Mean StDev SE Mean
Hours 25 6.640 1.075 0.215
Variable 99.0% CI T P
Hours ( 6.038, 7.242) -1.67 0.107
For hypothesis test, we have
H0: Average number of sleep hours of college students in the north-eastern United States is 7 hours.
Ha: Average number of sleep hours of college students in the north-eastern United States is not 7 hours.
H0: µ = 7 vs. Ha: µ ? 7 (two tailed test)
? = 0.05
Test statistic = t = -1.67
P-value = 0.107
P-value > ? = 0.05
So, we do not reject the null hypothesis that that Average number of sleep hours of college students in the north-eastern United States is 7 hours.
There is sufficient evidence to conclude that Average number of sleep hours of college students in the north-eastern United States is 7 hours.