1. Suppose a researcher is interested in the effectiveness in a new childhood ex

Question

1. Suppose a researcher is interested in the effectiveness in a new childhood exercise program mplemented in a SRS of schools across a particular county. In order to test the hypothesis that the new program decreases BMI (Kg/m2), the researcher takes a SRS of children from schools where the program is employed and a SRS from schools that do not employ the program and compares the results. Assume the following table represents the SRSs of students and their BMIs. Assuming that all the necessary conditions are met (normality, independence, etc.) carry out the appropriate statistical test to determine if the new exercise program is effective in reducing BMI. Use the equal varia procedure and assume a- o.05. (10pts) nce BMI (kg/m2) Student Student Intervention Group BMI (kg/m2) Control Group 20.3 18.2 20.5 19.5 21.6 19.5 19.4 20.6 22.4 1) Hypotheses Ho: Ha: 2) Test Statistic (show all steps for equal variance) sp2 = t-stat- B) P-Value 4) Conclusion

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 < mu2

where mu1 and mu2 are two population means for intervention group and control group respectively.

Assume alpha = level of significance = 0.05

Here sample size is too small and sample data is given so we use two sample t-test assuming equal variances.

We can do two sample t-test in MINITAB.

steps :

ENTER data into MINITAB sheet --> STat --> Basic statistics --> 2-Sample t --> Samples in different columns --> First : select intervention group --> Second :select control group --> Click on assume equal variances --> Options -->Confidence level : 95.0 --> Test difference : 0.0 --> ALternative : < --> ok --> ok

Two-Sample T-Test and CI: BMI intervention group, BMI control group

Method

Equal variances are assumed for this analysis.

Descriptive Statistics

Estimation for Difference

Test

Pooled SD = 1.200

Test statistic = -1.67

P-value = 0.067

P-value > alpha

Accept H0 at 5% level of significance.

Concllusion : There is sufficient evidence to say that two population means are equal.

: mean of BMI intervention group µ: mean of BMI control group Difference: - µ

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