Question

A researcher hypothesizes that arousal levels will be affected by meditation. The sample participates in formal meditation classes for 3 weeks, before and after which arousal is measured.

Subject                      BEFORE MEDITATION                               AFTER MEDITATION

1                                                  72                                                                           91

2                                                  162                                                                       155

3                                                  145                                                                       152

4                                                  183                                                                       190

5                                                  123                                                                       134

6                                                  167                                                                       157

7                                                  76                                                                           99

8                                                  112                                                                       104

9                                                  124                                                                       143

10                                               137                                                                       156

6. Please analyze the data using the appropriate hypothesis test on SPSS and cut and paste your SPSS results here:

7. Based on your SPSS results, do you reject or fail to reject the null?

_____________________________________________

8. Please write the “statistical statement” for your SPSS results:

9. Please write your results in a “literature” or “research study” format:

Answer 1

Performing analysis in SPSS as well as manual

Enter the three variables named Subjects, Before,After in variable view and enter the data in data view

Go to Analyze --> Compare means --> Paired sample t test

Select before and after together and send it to Paired variable box.

Click on OK

Screenshot of SPSS

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ_D​ = 0 i.e arousal levels are not affected by meditation

Ha: μ_D​ ≠ 0 i.e arousal levels are affected by meditation

This corresponds to a two-tailed test, for which a t-test for two paired samples be used.

Output

Paired Samples Statistics
		Mean	N	Std. Deviation	Std. Error Mean
Pair 1	Before	130.1000	10	36.76487	11.62607
	After	138.1000	10	31.27104	9.88877

Paired Samples Correlations
		N	Correlation	Sig.
Pair 1	Before & After	10	.945	.000

Paired Samples Test
		Paired Differences					t	df	Sig. (2-tailed)
		Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
					Lower	Upper
Pair 1	Before - After	-8.00000	12.49000	3.94968	-16.93480	.93480	-2.025	9	.073

Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=9.

Hence, it is found that the critical value for this two-tailed test is tc​=2.262, for α=0.05 and df=9.

The rejection region for this two-tailed test is R={t:∣t∣>2.262}.

Test Statistics

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

Decision about the null hypothesis

Since it is observed that ∣t∣=2.025 ≤ tc​=2.262, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.0735, and since p=0.0735≥0.05, it is concluded that the null hypothesis is not rejected.

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.

Hence

arousal levels are not affected by meditation