Reference no: EM132392867

In a study conducted in New Zealand, Parkin et al. randomly assigned volunteers to either wear socks over their shoes (intervention) or wear usual footwear (control) as they walked downhill on an inclined icy path. Researchers standing at the bottom of the inclined path measured the time (in seconds) taken by each participant to walk down the path. Here are the summary statistics. Note that the data are fairly symmetric in both groups.

n Mean SD

Intervention | 14 | 40.7 | 10.26 |

Control | 14 | 38.5 | 10.65 |

The research question to be addressed through the following questions is: Do the data provide evidence that people wearing socks over their shoes will take a shorter time to walk down an icy, steeply inclined road, on average, compared to those wearing usual footwear?

1.Select the parameter of interest in the context of this study.

A. The long-run average difference in the time it took participants to walk down the icy path

B. The preference of socks over the shoes for walking down an icy path

C. The preference of usual footwear for walking down an icy path

D. The distance covered when walking down an icy path

2.State the null and the alternative hypotheses in the context of the study.

A. Null: The long-run average time is the same in both groups. Alt: The long-run average time it took in the intervention group is less than the control group.

B. Null: The long-run average time is the same in both groups. Alt: The long-run average time it took in the intervention group is different from the control group.

C. Null: The long-run average time is the same in both groups. Alt: The long-run average time it took in the intervention group is more than the control group.

3.Name the appropriate theory-based method you would use to test the hypotheses stated in part (b).

A. p-value  t-test

B. Two-sample t-test

C. One proportion test

4.State the validity conditions that have to be met to be able to perform the test named in part (c). Are these conditions met?

A. Yes, because even though the sample sizes are less than 20, the data are symmetrically distributed in each group

B. No, because even though the sample sizes are more than 20, the data are skewed in each group

5.Regardless of your answer to part (d), perform the theory-based test proposed in part (c) and find the t statistic and p value. 

(Round the test statistic to 2 decimal places, e.g. 1.58, and the p-value to 3 decimal places, e.g. 0.586.)

t=_______

p=______

6.Determine a 95% confidence interval for comparing the walking time between the two groups. (Round your answers to 4 decimal places, e.g. 0.5863.)

( __________ , __________ )

7.Summarize your conclusions about the research question of the study.

A. We do not have strong evidence that the average walking time is significantly less for the intervention group. However, we can't determine cause and effect or generalize to a broader population because there might be other confounding factors.

B. We have strong evidence that the average walking time is significantly less for the intervention group. Because our results are not significant, we can't determine cause and effect or generalize to a broader population.

C. We do not have strong evidence that the average walking time is significantly less for the intervention group. Because our results are not significant, we can't determine cause and effect or generalize to a broader population.

D. We have strong evidence that the average walking time is significantly less for the intervention group. However, we can't determine cause and effect or generalize to a broader population because there might be other confounding factors.