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# Inferential Statistic: T-Test

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1.) A student wants to study the effect of two different nursing care models on quality scores of a several units in a hospital. The possible quality scores that the units can have are from 1 to 5, with 1 being the lowest and 5 the highest. One nursing care model involves a decentralization of tasks to a team of licensed and unlicensed nurses (the "team" approach). The other model involves hiring mostly RNs who do most of the care for the patients with some assistance from nursing assistants (the "primary care" approach). The student assigns 6 units in a hospital to use the team model for a period of a year, and 6 units to use the primary care model. At the end of the year she assesses each unit's quality score. She finds that the mean quality score for the 6 units using the team model is 3.8 and the mean quality score for the 6 units using the primary care model is 4. She assumes that the population variances for the two groups are the same and she calculates a pooled variance of 1 for the two samples.

Can this student reject a null hypothesis that there is no difference in quality scores between the two groups of units?

2.)You need to use the t distribution as your null hypothesis distribution whenever
the population mean and variance are unknown.
the population mean is unknown and the sample size is small.
the population mean is small and the sample size is unknown.
the population variance is unknown and the sample size is small.
none of the above.

3.)You read an article where the correlation coefficient was reported as being 0.28, and this was reported as being statistically significant. What do you think this means?
The correlation was curvilinear.
the sample size was large
there was a large outlier.
all of the above.
none of the above.

https://brainmass.com/statistics/statistical-inference/inferential-statistic-t-test-565155

#### Solution Summary

The solution provides step by step method for the calculation of t statistic. Formula for the calculation and Interpretations of the results are also included.

\$2.19

## Inferential Statistics Using T-Test

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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