4. Recent research has demonstrated that music-based physical training for elder

Question

4. Recent research has demonstrated that music-based physical training for elderly people can improve balance, walking efficiency, and reduce the risk of falls (Trombetti et al., 2011). As part of the training, participants walked in time to music and responded to changes in the music’s rhythm during a 1-hour per week exercise program. After 6 months, participants in the training group (n = 12) increased their walking speed and their stride length compared to individuals in the control group (n = 12). A t-test was conducted to compare differences in scores between the categories and a value of -2.76 was obtained.

A. State the null and the alternative hypothesis (using words and symbols)

B. Set the decision criteria

C. Use the t-value provided (you don’t need to do calculations).

D. Make the decision (fail to reject or reject the null hypothesis at either or both the .01 or .05 alpha level)

Explanation / Answer

Part A

The null and alternative hypothesis is given as below:

Null hypothesis: H0: There is no any significant difference in the balance, walking efficiency and reduce the risk of falls for elder people due to the music based physical training.

Alternative hypothesis: There is a significant difference in the balance, walking efficiency and reduce the risk of falls for elder people due to the music based physical training.

H0: µ1 = µ2 v/s Ha: µ1 µ2

This is a two tailed test.

Part B

The decision criteria are given as below:

We reject the null hypothesis if the p-value is less than the given level of significance or alpha value and we do not reject the null hypothesis if the p-value is greater than the given level of significance or alpha value. We reject the null hypothesis if the test statistic value is greater than the critical value and we do not reject the null hypothesis if the test statistic value is less than the critical value.

Part C

We are given

Test statistic value = t = -2.76

Sample size = n = 12

So, degrees of freedom = n – 1 = 12 – 1 = 11

P-value = 0.0186

Consider Alpha value = 0.05

Part D

Here, P-value < Alpha value

So, we reject the null hypothesis

This means we conclude that there is sufficient evidence that there is a significant difference in the balance, walking efficiency and reduce the risk of falls for elder people due to the music based physical training.

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