Question

Average Sleep Time on a School Night	Students
4 hours	8
5 hours	9
6 hours	14
7 hours	12
8 hours	15
9 hours	4
10 hours	0

Ho: 72.7% of high school students (grade 9-12) do not get enough sleep at night. (minimum 8 hours) (article claim)

Ha: 72.7% of high school students (grade 9-12) do get enough sleep at night.

Record the hypothesis test. Use 5% level of significance Include 95% confidence interval on solution sheet.

Create graph to illustrates results.

Conclusion about article claim in light of your hypothesis test.

Sentence interpreting your confidence interval in the context of the situation.

Answer 1

We can this as an example of binomial distribution. The two outcomes are students who get enough sleep (8 or more hours) and students who do not get enough sleep.(less than 8 hours.) Since the minimum requirement for enough sleep is 8 hours.

Average Sleep Time on a School Night	Students
4 hours	8	43
5 hours	9
6 hours	14
7 hours	12
8 hours	15	19
9 hours	4
10 hours	0
Total		62

The third column is the sum of students who get enough sleep or not based on the criteria.

We can take 'X' as the number of students who do not get enough sleep. Therefore 'p' is the population proportion that they do get enough sleep.

Ho: 72.7% of high school students (grade 9-12) do not get enough sleep at night. (minimum 8 hours) (article claim)

p = 72.7%

Ha: 72.7% of high school students (grade 9-12) do get enough sleep at night.

p 72.7%

X= 43 n = 62

Sample proportion

Test Stat =

Where the null proportion = 72.7%

test Stat = -0.571

Critical value at 0.05

We will use a normal approximation since the 'n' is large (>30). Also since it is two tailed (cecking for difference on either sides) we divide level by 2. The value is calculated using normal percentage tables at p = 2.5%

Critical value = 1.96

Since |Test stat|<Critical value

We do not reject the null hypothesis and conclude that the 72.7% significantly do not get enough sleep.

The confidence interval for population proportion is given by

Where

We can say with 95% certainty that the true proportion of students who do not get enough sleep lies within 0.579 - 0.808.

Here as we can see that interval has 72.7% (null value), we donot reject the null hypothesis.

In th graph we can see that

-1.96 < -0.571 <1.96 that is the z-score lis within the retaining region.