# Exploring t-Tests and Confidence Intervals for Continuous Data

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Question description

n this discussion, we will investigate confidence intervals and t tests for continuous data. To do this, we will revisit the TAA data that you studied in the Week Three assignment.

You may recall from the Week Three assignment that you have available data on 12 tumor-associated antigens (TAAs), from 90 normal individuals (controls) and 160 hepatocellular carcinoma patients (cases). These data are in the Excel file MHA610_Week 3_Assignment_Data.xls; the levels of the 12 TAAs are given in the columns with headings Ab14, HCC1, IMP1, KOC, MDM2, NPM1, P16, P53, P90, RaIA, and Survivin.

• First, randomly select three of the 12 TAAs for further study.

• Next, Perform two sample t-tests for comparing the levels of each of your three TAAs between the cases and the controls.

• Then, Use the t-tests to order the TAAs in terms of relative ability to discriminate between the cases and controls, from best to worst discriminator. Is this ordering helpful if you want to select a subset of TAAs to discriminate between cases and controls?  Assume for now that you can judge the relative merits of your three TAAs by the magnitudes of their respective two-sided p-values from the two sample t-tests, so that your best discriminator is the TAA with the smallest p-value.

• Lastly, Construct and report 95% confidence intervals for the mean level of your best TAA discriminator in the controls, the mean level of your best TAA discriminator in the cases, and the difference in mean levels (cases - controls). Discuss whether your confidence intervals are concordant with the t-tests.

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