In the HW7 folder of the course website, there is a CSV file called Prison.csv, which includes sentence lengths (in years) for a sample of White and Black defendants. A criminologist collected these data because they are interested in whether there was any disparity in sentencing based on the race of the defendant. Specifically, they selected a random sample of 18 burglary convictions and recorded the prison terms given to the 10 white defendants and the 8 black defendants sampled. Using these data and a 0.05 alpha level, test the null hypothesis that Whites and Black defendants convicted of burglary in this jurisdiction do not differ with respect to prison sentence length.

a. (0.125 points) In symbols and not words, what is the null hypothesis for this test? ______________________________________________________________________________

b. (0.125 points) In symbols and not words, what is the alternative hypothesis for this test? ______________________________________________________________________________

c. (0.125 points) Is this a one-sided or two-sided test? How do you know? ______________________________________________________________________________

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d. (0.125 points) Will you use a z-test or a t-test in this situation? Why? ______________________________________________________________________________

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e. (0.25 points) What is the p-value calculated from the sample results?

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f. (0.25 points) What decision about the null hypothesis does your test lead to?

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g. (0.875 points) If you increased your sample sizes by five times so that you had 50 White defendants and 40 Black defendants, but the group means and standard deviations remained the same, would you reach the same conclusion about the statistical significance of the racial difference in sentencing? Report the numbers used to make your decision. (NOTE: This question may require you to work with the data by hand instead of using built-in Google Sheets commands.) ______________________________________________________________________________

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White Defendants,Black Defendants 3,4 5,8 4,7 7,3 4,5 5,4 6,5 4,4 3, 2,

above is the CSV file called prison csv

PLEASE show your work