Question

The amount of oxygen consumption was measured in seven individuals over two periods of time while sitting with their eyes closed. During the first period, they listened to an exciting adventure story; during the second period of time, they heard restful music. The researcher is not sure whether participants will consume more or less oxygen during the story compared with the music. Here are their results:

Subject	Story	Music
1	5.8	5.3
2	8.1	7.2
3	6.4	6.3
4	7.8	6.1
5	4.6	5.1
6	5.1	4.8
7	6.6	6.1

1. Use the 5 steps of hypothesis testing
   1. Use excel (include populations & hypotheses in excel document)
2. Sketch the distribution with cut-off value (s) and sample score, and regions of acceptance and rejection labeled.
3. Summarize what you found.

Answer 1

B)

SOLUTION A: STEP 1 NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=6.

Hence, it is found that the critical value for this two-tailed test is tc​=2.447, for α=0.05 and df=6.

The rejection region for this two-tailed test is R={t:∣t∣>2.447}.

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis: Since it is observed that ∣t∣=1.936≤tc​=2.447, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.1009, and since p=0.1009≥0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.

c) We don't have sufficient evidence to conclude that participants will consume more or less oxygen during the story compared with the music.