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In general, high school and college students are the mostpathologically sleep-deprived segment of the population. Theiralertness during the day is on par with that of untreatednarcoleptics and those with untreated sleep apnea. Notsurprisingly, teens are also 71 percent more likely to drive drowsyand/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 25college students at a small college in the northeastern UnitedStates slept and is from a random sample. Enter this data into C1of Minitab Express.

6 9 7 7 6 7 7 5 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%, and99% as the confidence levels for the confidence interval.

·      5% as the level of significance( ) for the hypothesis test.

·         7 hours sleepas the null hypothesis (according to The Sleep Foundation).

a.    List the three (3) assumptions for a validconfidence interval and hypothesis test. Provide an explanation asto whether or not each one is met - more than just a simple “yes”or “no” – and refer to the boxplot and normal probability plot, asnecessary, in your assessment.

b.    What degrees of freedom will you use forthe t distribution? Show your calculation.

(Hint: degrees of freedom is n-1.)