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Inferential Statistics Using T-Test

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A student studied the effect of diabetic disease management on patients' A1C blood test results. The student placed 22 new diabetic patients that presented at a local clinic into two groups: 12 were placed in a group in which the patients received the usual treatment plus they additionally received disease management care; 10 were placed in a group in which the patients received the usual treatment only. After 6 months the student measured A1C levels of the patients in both groups. The mean A1C blood level for the 12 patients in the treatment group was 7%, with an unbiased variance of 1. The mean A1C blood level for the 10 patients in the control group was 8.5% with an unbiased variance of 1.

1.) What is the pooled variance for these two groups?

2.)Using the pooled variance you calculated in question # 1, what is the t value for the t test that compares the AIC levels of the treatment group to the control group?

3.)The student wishes to test the null hypothesis is that there is no difference in A1C levels (the alternative hypothesis that there is a difference in A1C levels between the 2 groups). What is the critical t value for a t test that is testing the difference between the two groups at a 0.05 level of significance?

4.) The student wishes to know whether there is a difference in A1C levels between the 2 groups (the null hypothesis is that there is no difference in A1C levels). Are the A1C blood levels of the treatment group significantly different than those of the control group at a 0.05 level of significance? (Use the t value that you calculated in question # 2 and the critical t value you found in question #3.)

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Solution Summary

The solution contains step-by-step calculations and explanations to determined pooled variance and test the null hypothesis.

Solution provided by:
Anwesha Ghosh, MSc
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  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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