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).

c. What degrees of freedom will you use for the t distribution? Show your calculation.

Answer 1

n= 25

Sample mean:

Sample standard deviation:

The degree of freedom= n-1=24

Confidence interval:

90% Confidence interval:

95% Confidence interval:

99% Confidence interval:

At 5% significant level, 7 is in confidence interval range. So, we can conlude that the test statistic is statistically equal to 7 and fail to reject H0.

Using above confidence interval, 7 is within interval range. So, we can conlude that the sample mean is statistically equal to 7 and fail to reject H0. The test statistic is not significant.

Minitab output: