PART ONE:
Situation One: It has been reported that the mean amount of sleep that adults receive is 7 hours per night. Your boss has asked you to investigate this statistic by conducting your own study. You gather 49 adults and find the following information. The mean amount of sleep was 6.2 hours with a standard deviation of 1.8 hours. Based on your results, you claim that adults receive less than 7 hours of sleep. Test your claim with a 0.05 significance level.
1
- Identify the Claim: Adults receive less than 7 hours of sleep. 2
- Give Symbolic Form: H
0
:μ > 7
3
- Identify Null and Alternative Hypothesis
Null (
H
0
) Hypothesis: Adults, on average, receive 7 hours of sleep. H0:μ = 7
Alternative (H
a
) Hypothesis: Adults, on average, receive less than 7 hours of sleep. H
0
:μ < 7
4
- Select Significance Level: 0.05
5
- Identify the Test Statistic: -3.1116
(6.2-7)/1.8/ √49 6.2= sample mean, 7= 06 - Choose a Testing Method: 0.00156527 SEE
EXCEL FOR WORK. P-value Method
Critical Value Method
7
- Make a Decision
Reject H
0
8
- Restate Decision in Non-technical Terms
There is sufficient evidence at the 0.05(α) level of significance to support the claim that adults receive less than 7 hours of sleep.
Situation Two: Your boss also would like you to look at average sleep for a specific age range (between 35 and 44 years of age). It has been previously reported that 38.3% of adults in this age
range receive the recommended amount of sleep per night (at least 7 hours). You decide to test this claim by gathering 32 adults between the ages of 35 and 44 years old. In the sample, you find that 15 of the participants receive at least 7 hours of sleep. Test the claim that more than 38.3% of adults get the recommended amount of sleep per night with a significant level of 0.01.
1
- Identify the Claim: 38.3% of adults in the age range of 34-44 years receive the recommended amount of sleep per night of at least 7 hours. 2
- Give Symbolic Form
H
0
= 38.3
