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). Use Minitab Express to: (i) create a boxplot – GRAPHS, Boxplot - and (ii) normal probability plot – GRAPHS, Probability Plot, and (iii) calculate descriptive statistics - STATISTICS, Describe, Descriptive Statistics. Under the “Descriptive Statistics” dialog window, click on the Statistics tab and check only Mean, SE of mean, Standard deviation, and N. Include these with the submission of your project

Use Minitab Express to: (i) create a boxplot – GRAPHS, Boxplot - and (ii) normal probability plot – GRAPHS, Probability Plot, and (iii) calculate descriptive statistics - STATISTICS, Describe, Descriptive Statistics. Under the “Descriptive Statistics” dialog window, click on the Statistics tab and check only Mean, SE of mean, Standard deviation, and N. Include these with the submission of your project.

Answer 1

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.

The data set is as follows:-

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

The given level of significance is 5%.

i.) The box plot of our given data set is as follows:

Observation: The median hours of sleep is 7 hours.There are presence of outliers who sleep very less,about 4 hours.Also the distribution of the hours of sleep is positively skewed which means that the number of students with greater sleep hours is more in the sample.

ii.) The Normal Probability Plot of the given data for a 95% level of confidence is :

iii.) The decriptive statistics for our given data are as follows: -

Variable        Mean    SE Mean    StDev
Hours of Sleep    6.640    0.215        1.075

Observation :

The average of hours of sleep of the sample of 25 students is 6.64 hours.

The SE of the mean which means the Standard Error of the mean is 0.215, ie the variablity of the sample mean is 0.215 which is very less.

The standard deviation of the sample data is 1.075, which shows that the variability of the observations in our sample is 1.075 which is very less.In other words, the hours of sleep of the students in the sample is more or less consistent for the students.