Question

Although it is generally assumed that routine exercise will improve overall health, there is some question about how much exercise is necessary to produce the benefits. To address this question, a researcher obtained 20 pairs of participants, matched on age, gender, and weight. All participants exercised regularly but one participant within each pair exercised less than two hours per week, and the other spent more than five hours per week exercising. Each participant was subsequently evaluated by a physician and given an overall rating of their health. The researcher runs the statistics using SPSS and obtains the output below:

T-Test

PAIRED SAMPLE STATISTICS

	mean	N	STD. Deviation	Std. error Mean
pair two_hrs	13.40	20	2.563	.573
1 five_hrs	14.45	20	2.235	.500

Paired Samples Test

	Paired Differences	Paired Differences	Paired Differences	PairedDifferences 95% confidence interval of the differences				...
	Mean	Std. Deviation	Std Error mean	Lower Upper	t	df	Sig.(2-tailed)
Pair 1 two_hrs-five_hrs	-1.050	2.038	.456	-2.004 -.096	-2.304	19	.033

1) using the hypothesis, what is the null hypothesis and the alternative hypothesis? and should it be rejected, why or why not?

2) what is the dependent and independent variable?

3) Is this a between-subjects or within-subjects design?

4) What is the effect size? Please explain your answer.

Answer 1

Solution:

1) using the hypothesis, what is the null hypothesis and the alternative hypothesis? and should it be rejected, why or why not?

Answer:

Let denotes the mean of the differences of the rating for two groups.

The null and alternative hypotheses are:

The null hypothesis should be rejected because the p-value is 0.033, which is less than the significance level of 0.05.

2) what is the dependent and independent variable?

Answer: The dependent variable is overall health rating and the independent variable is hours of exercise per week

3) Is this a between-subjects or within-subjects design?

Answer: This is a within-subjects design because the given data is matched paired individuals under study.

4) What is the effect size?

Therefore, the effect size indicates there is a medium effect