Question

Sample 8 people and ask how many hours of sleep they got last night. Then conduct a hypothesis test if the mean hours of sleep last night is less than 8 hours. Use significance levels of ? = 0.05, 0.01, and 0.10.

1. List the data values, sample mean and sample standard deviation.

2. Conduct a Hypothesis Test including each of the four steps.

Answer 1

Let the sample of sleep hours for 8 people are,

sample	Sleep hours
1	5
2	6
3	8
4	9
5	7
6	5
7	6
8	4

The mean and standard deviation of the data values is calculated as,

2)

A single sample t test is used to compare the mean hours of sleep of sample with a hypothesized population mean. The null hypothesis is defined as,

Null hypothesis: There is no difference between sample mean and population mean, i.e.

Alternate hypothesis: There is a significant difference between sample mean and population mean, i.e.

This is a two tailed test. And the test statistic is obtained as follow,

The t critical values can be obtained using the t distribution table for degree of freedom = 8-1=7 and for signigficance level = 0.01, 0.05, 0.10.

Decision Rule: The null hypothesis is rejected if t-value is less than t-critical value.

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