You are the manager of a local rehab center and you were asked to assess its eff

Question

You are the manager of a local rehab center and you were asked to assess its effectiveness. You conducted an experiment where you randomly assign eligible clients to experimental and control groups. You hypothesize the program will be effective in reducing the weekly number of people who fail the program. Use the data below to answer the following questions the standard deviation for the experimental group is 1.07 and the standard deviation for the control group is 1.14
Experimental Control Group Group
7 5 5 6 6 4 5 3 8 4 5 3 6 6 7 3
a. State the null and research hypotheses b. Indicate the appropriate statistical test c. With the significance level set at .10, specify your critical value d. Report the obtained value e. Declare your decision (i.e., whether to reject or retain the H0) f. Explain your decision You are the manager of a local rehab center and you were asked to assess its effectiveness. You conducted an experiment where you randomly assign eligible clients to experimental and control groups. You hypothesize the program will be effective in reducing the weekly number of people who fail the program. Use the data below to answer the following questions the standard deviation for the experimental group is 1.07 and the standard deviation for the control group is 1.14
Experimental Control Group Group
7 5 5 6 6 4 5 3 8 4 5 3 6 6 7 3
a. State the null and research hypotheses b. Indicate the appropriate statistical test c. With the significance level set at .10, specify your critical value d. Report the obtained value e. Declare your decision (i.e., whether to reject or retain the H0) f. Explain your decision
Experimental Control Group Group
7 5 5 6 6 4 5 3 8 4 5 3 6 6 7 3
a. State the null and research hypotheses b. Indicate the appropriate statistical test c. With the significance level set at .10, specify your critical value d. Report the obtained value e. Declare your decision (i.e., whether to reject or retain the H0) f. Explain your decision Experimental Control Group Group
7 5 5 6 6 4 5 3 8 4 5 3 6 6 7 3
a. State the null and research hypotheses b. Indicate the appropriate statistical test c. With the significance level set at .10, specify your critical value d. Report the obtained value e. Declare your decision (i.e., whether to reject or retain the H0) f. Explain your decision

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 not= mu2

where mu1 and mu2 are two population means of experimental group and control group respectively.

Assume alpha = level of significance = 0.10

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

We can do two sample t test in EXCEL.

ENTER data into EXCEL sheet --> Data --> Data Analysis --> t-test : Two-Sample Assuming Equal Variances --> ok --> Variable 1 Range : select experimental group data --> Variable 2 Range : select control group data --> Hypothesized mean : 0 --> Alpha : 0.10 --> Output Range : select one empty cell --> ok

Test statistic = 3.11

Critical value = 1.345

P-value = 0.0077

P-value < alpha and test statistic > critical value

Reject H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that the two population means differ.

t-Test: Two-Sample Assuming Equal Variances experimental group control group Mean 6.125 4.25 Variance 1.267857143 1.642857143 Observations 8 8 Pooled Variance 1.455357143 Hypothesized Mean Difference 0 df 14 t Stat 3.108468544 P(T<=t) one-tail 0.003850869 t Critical one-tail 1.345030374 P(T<=t) two-tail 0.007701737 t Critical two-tail 1.761310136

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