A survey of 656 boys and girls who were 13 to 18 years old asked about adequate

Question

A survey of 656 boys and girls who were 13 to 18 years old asked about adequate sleep and other health related behaviors. The recommended amount of sleep is six to eight hours per night. In the survey 54% of the respondents reported that they got less than this amount of sleep on school nights. An exercise scale was developed and was used to classify the students as above or below the median in this domain. Here is the 2 times 2 table of counts with students classified as getting or not getting adequate sleep and by the exercise variable. The null hypothesis is that there is no relationship between exercise and sleep. The alternative is that these two variables are related. a.Find the distribution of adequate sleep for the high exercisers. b.Do the same for the low exercisers. c.Summarize the relationship between adequate sleep and exercise using the results from parts (a) and (b). d.Find the expected counts and use them to compute the Chl-square statistics. e.Compare your Chi

Explanation / Answer

(a) Of the high exercisers, 151 / (151+148) = 50.5% get enough sleep, and the rest (49.5%) do not.

(b) Of the low exercisers, 115/(115+242) = 32.2% get enough sleep, and the rest (67.8%) do not.

(c) Those who exercise more than the median are more likely to get enough sleep.

(d) The expected frequencies are

The chisquare value is calculated as the following table

Test statitic chisquare value = 22.577

e) The critical value of the test is 3.8414 at 5% and 1df

Here Chisquare value > chisquare critical value and P value = 0.000 < alpha (0.05) we reject H0

f) We conclude that the two variables are related

Enough Sleep High Low Total Yes 121.2409 144.7591 266 No 177.7591 212.2409 390 Total: 299 357 656

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