As a researcher, you are curious if low income impacts the length of prison sentences for theft. The known average sentence is general population is µ = 12.5 months. You have a random sample of 49 people (N = 49) 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 sx = 4.3. In this case, the critical values for an α (alpha) = .05 are +/- 2.01.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. 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?

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 31PPS

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As a researcher, you are curious if low income impacts the length of prison sentences for theft. The known average sentence is general population is µ = 12.5 months. You have a random sample of 49 people (N = 49) 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 = 4.3. In this case, the critical values for an α (alpha) = .05 are +/- 2.01.

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. 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?

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