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)

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

Sample size:

Sample mean:

Sample deviation:

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

Create graph to illustrates results.

Answer 1

Here Test for population proportion can be used.

Where P is the population proportion of students not getting minimum 8 hours of sleep

Sample size=62

Sample mean

Sample variance

Sample standard deviation =0.3463

Test statistic

Where p is the sample proportion, P is the population proportion, Q=1-P. and n= sample size

In the sample given proportion of students not getting minimum 8 hours of sleep is

P=0.727 and Q-1-0.727=0.273.

Z-critical value is 1.96

Hence we accept the null hypothesis that 72.7% of students are not getting minimum 8 hours of sleep.

95% confidence interval is

=(0.58265, 0.80444)

From the graph we can see that more than 85% of the students are getting less than 8 hours of sleep.