Question

Music Group		Control Group
30	28	30	23
32	25	23	26
28	30	24	20
26	29	29	20
30	28	26	26
20	27	20	21
24	29	26	23
33	27	21	20
31	26	22	26
26	28	25	27
30		27

SPSS.1 A study reveals that older adults work out a little harder when they listen to music. The table below contains the data from two groups of older adults: one group listened to music while walking; the other group did not listen to music. Stride length was measured as an indicator of how hard they were working out (higher numbers = longer stride = working out harder).

What are the sample means in this study?

                                                                      M_music =                   M_control =

SPSS.2 Paste your SPSS output of the descriptive statistics below.

SPSS.3 What t statistic was obtained (calculated) for the music and exercise study.

SPSS.4 Assuming a two-tailed hypothesis test with alpha = .05, use your t-table to look up the critical t-value for this study. What are the critical t-values?

SPSS.5 What p-value is obtained from your SPSS output?

SPSS.6 Is there a statistically significant effect of music on stride length?

Answer 1

Solution:

Here, we have to use two sample t test or independent samples t test for population means. The SPSS output for this test is given as below:

Group Statistics
	Group	N	Mean	Std. Deviation	Std. Error Mean
Stride	Music Group	21	27.9524	2.92363	.63799
	Control Group	21	24.0476	3.07370	.67074

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
Stride	Equal variances assumed	.776	.384	4.218	40	.000	3.90476	.92570	2.03386	5.77567
	Equal variances not assumed			4.218	39.900	.000	3.90476	.92570	2.03371	5.77581

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: There is no any statistically significant effect of music on stride length.

Alternative hypothesis: H_a: There is a statistically significant effect of music on stride length.

Means for both groups are given as below:

M_music =27.9524

M_control =24.0476

Test statistic is given as below:

t statistic = 4.218

α = 0.05

Critical t-values = ±2.0227

[Critical t values = -2.0227 and 2.0227]

(by using t-table)

P-value = 0.000

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a statistically significant effect of music on stride length.