As a researcher, you are curious if income impacts the length of prison sentences for theft. The known average sentence for the general population is = 12.5 months. You have a random sample of 81 people (N = 81) whose income is below the poverty line. The average sentence for this sample of people was xbar = 16.8 months, with a standard deviation of s_x = 5.3. In this case, the critical values for an (alpha) = .05 are +/- 1.99 (6 points).

A) Please calculate and report the confidence interval for these data, including your level of confidence.

Hints:

• Do not calculate a z/t-statistic.
• Remember, the interval is centered on a descriptive statistic, such as xbar.
• You have been provided with the standard deviation of the sample. You will need to use this to calculate standard error.
• The level of confidence is a specific percentage based on alpha; high or low are NOT answers.

B) Based on the confidence interval, would you retain or reject the null hypothesis? Explain your reasoning.

C) Would the p-value be bigger or smaller than alpha?

D) In everyday language, what do these results tell you about the research question? What can we conclude about income and prison sentences?

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A researcher wants to determine if a new schizophrenia drug has different effects on patients compared to a placebo. A total of n₁ = 20 people took the new drug for six weeks and n₂ = 20 people took a placebo for 6 weeks. She then assesses their symptoms. The group of participants who took the new drug showed an average of xbar₁ = 7.4 major symptoms a day after the six weeks, with a standard deviation of S₁ = 2.6. The group of participants who took the placebo displayed on average of xbar₂ = 7.6 major symptoms a day after the six weeks, with a standard deviation of S₂ = 2.2 (7 points).

A) Please calculate and report the appropriate statistic, showing all your steps.

B) Based on an alpha = .05, critical values of +/- 2.06, and obtained (calculated) the test-statistic from part A, should you retain or reject the null hypothesis?

C) Would the p-value be bigger or smaller than alpha?

D) Please construct and interpret the follow-up confidence interval that would be the most appropriate for these data. Hint: does the interval contain the null value for this type of test?

E) In everyday language, what do these results tell you about the research question? Does which drug someone takes (real versus placebo) impact their symptoms?