Applied Statistics Math 810 - POWERPOINT

Submitted

Applied Statistics Math 810

Running head: MINI PROJECT 1 1

MINI PROJECT 1 4

Table of Contents

Executive Summary 3

Introduction 3

Discussion of Results 3

Answer 1 3

Answer 2 4

Answer 3 5

Answer 4 5

Conclusion 6

Reference 7

Appendices 8

The report analyzes the statistical tools required to detect the impact of different training programs on reducing the BMI of moderately overweighed adolescents. To analyze the variances within the populations, different statistical tools such as independent t-test, ANOVA, F-test and such others were used. The results showed that moderate weight resistance training program was the most effective method for BMI reduction, whereas, cardiovascular exercise program was not found to be effective in case of BMI reduction.

The following project of applied statistic aims at finding the effects of exercise intervention with the adolescents. The assignment includes a few questions which will be answered using suitable statistical methods in the attached excel sheet. The data set contains the BMI readings for 216 moderately overweight teens that were divided equally in four groups A, B, C and D. Each group was given a different method of exercise to reduce their body weight. The results will highlight the most suitable exercise for reducing weight.

a) The average changes in each group can be seen below-

The hypothesis has been tested in this segment using the confidence intervals. This method is used to determine a range of values among which population of interest lies. The confidence interval selected in this case was 95%. The calculations showed that the difference between the upper and lower confidence levels is significant in Group B, C and D whereas in Group A, the difference is negligible. It shows that in case of Group A, null hypothesis cannot be rejected. Hence, the impact of cardiovascular exercise program has been least in case of BMI reduction. The average value of change in BMI also shows that the maximum change in the BMI was caused due to moderate weight resistance training program and least due to cardiovascular exercise program over the time period of three weeks.

b) The hypothesis test was performed using t-Test: Paired Two Sample for Means as this method is considered to be most effective if, before and after values of the same group are to be compared. As provided in appendix, the p-values for the four groups is as follows:

The test shows that the p-value of only Group A is higher than 0.05 and hence, there is not enough evidence to support the claim that average change in BMI for subjects in Group A is significant. The remaining groups have p-values less than 0.05 and thus, the three methods in Group B, C and D are effective in reducing BMI.

c) The results of both these methods are comparable as they both show that the impact of cardiovascular training on Group A has been least effective. Remaining three groups showed significant changes in BMI.

For this, the independent sample t-test was used as the results of two different populations were to be compared. In order to check whether equal or unequal variances are used, the F-test was conducted as it indicates the variances within or between the sample populations. The rejection region of the two tailed test lies between 0.582 and 1.712. The F-value of 6.174 does not lie between the rejection regions and thus, the null hypothesis is rejected. The results of F-test show that the population variance of Group A is significantly different from Group B (refer appendix).

According to t-test, the p-value of Group A (0.1733) is higher than 0.05 whereas the p-value of Group B (0.000) is lower than 0.05. Thus, it can be said that the weight resistance training program was more effective in reducing BMI than cardiovascular exercise.

To calculate the variances between the populations of two groups, F-test was conducted. The reason behind choosing the F-test is that it indicates the variances within or between the sample populations. The rejection region of the two tailed test lies between 0.575 and 1.728. The value of F-test obtained is 0.994. Since, the value lies in the rejection region, the null hypothesis is not rejected. The results of F-test show that the null hypothesis is not rejected and the population variance of Group C is not significantly different from the population variance in Group D, at the significant level of 0.05 (refer appendix).

a) For verifying whether the average starting BMIs (BMI_1) of the four groups were same or not, ANOVA has been conducted. ANOVA is used to test the variance between the populations of more than two groups. The results of ANOVA suggest that the p-value between the populations of the four groups is 0.7034, which is greater than significant value 0.05. Thus, the difference between the initial BMIs of the four groups is not significant.

b) It will have a positive impact on the reliability of the results. If the initial values of BMI are similar for all the four groups, the difference in the BMI values after 3 weeks can be distinguished and analyzed properly.

The assignment aimed at identifying the best method for reducing the BMI in the time period of three months. According to the tests, it can be said that the most effective method for BMI reduction is moderate weight resistance training program. The method which was not found to be significant enough in case of BMI reduction was cardiovascular exercise program. Comment by Dr. Harris: Good! Could also add that the BMI for each group should be confirmed to be similar before starting the experiment.

MINI PROJECT 1 2

Reference

Ott, R. L., & Longnecker, M. (2016). An introduction to statistical methods and data

analysis (7th ed.). Boston: Cengage Learning.

Appendix A: Tables

Answer 2

Answer 3

Answer 4

Anova: Single Factor

SUMMARY

GroupsCountSumAverageVariance

BMI_1 A 541484.427.48890.9546

BMI_1 B 561538.427.47141.0312

BMI_1 C 511407.927.60590.7266

BMI_1 D 551505.927.38001.1331

ANOVA

Source of VariationSSdfMSFP-valueF crit

Between Groups1.362630.45420.47010.70342.6472

Within Groups204.82392120.9662

Total206.1865215

Running head:

MINI PROJECT 1

1

Mini Project 1

Submitted

In partial fulfillment for

Applied Statistics Math 810

October 21

, 2018

Running head: MINI PROJECT 1 1

Mini Project 1

Submitted

In partial fulfillment for

Applied Statistics Math 810

October 21, 2018