homework 5 soc 10B 2023

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University of California, Irvine *

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SOC 10B

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Sociology

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Feb 20, 2024

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Soc/Anthro 10B: Probability and Statistics Homework #5 Significance test for a proportion with review of confidence interval for a proportion ***Make sure to submit only one file on Canvas. That means insert any images or other output into your homework assignment. Information for homework 5: Use the data from the 2018 General Social Survey, which can be loaded using the following command: load(url( " https://github.com/drschaef/10B-Files/blob/main/data_homework lab 10B _230304.RData?raw=TRUE ")) The data are a random sample from the adult population in the US. We will use the variable WRKGOVT. Variable Employer type WRKGOVT Survey question: (Are/were) you employed by the federal, state, or local government or by a private employer (including non-profit organizations)? Frequency Distribution Cells contain: Distribution -N of cases 1: GOVERNMENT 449 WRKGOVT 2: PRIVATE 1,765 COL TOTAL 2,214 2 points 1. Find the proportion of respondents who work for a government employer. This is the 10 points 2. proportion that you will use in the statistical analyses below. Show your calculations including the numbers you use to find the proportion of people who work for the government. The proportion of people who work for a government employer is equal to Draw a graph to show the distribution of responses to the question of where people work. Provide a title for the graph that gives the source of the data. Keep in mind that it is best practice to use percentages rather than frequency counts. Hint: You can copy and paste your graph here Suppose that your reading of professional research on the topic leads you to the hypothesis that the size of the government has increased over the past 30 years. Test that the proportion of adults working for a government employer has increased since 1985, when 18.1% of adults worked for a government employer. Use the variable WRKGOVT from the 2018 General Social Survey to investigate this hypothesis.

Soc/Anthro 10B: Probability and Statistics Homework #5 Significance test for a proportion with review of confidence interval for a proportion 6 points a. State the null hypothesis in words and in symbols In words In symbols 6 points b. State the alternative hypothesis in words and in symbols In words In symbols 6 points c. Are you using a one-sided (directional) or a two-sided (non-directional) alternative hypothesis? Explain why you are using that kind of hypothesis. 12 points d. Conduct the z test using R Commander. Copy and paste the relevant output below. 12 points e. Calculate the value of Z and report the P value that the software reports. For the Z statistic, show the numbers that were used to calculate it. (Hint what numbers are in the numerator and what numbers are in the denominator?) Z. statistic = P value = 10 points f. Using a .05 o-level (alpha level) what is your decision about the null hypothesis? 12 points 4. Find the 95% confidence interval for the proportion of adults in the US who work for a government employer. Report the upper and lower bounds of the interval: lower bound upper bound

Soc/Anthro 10B: Probability and Statistics Homework #5 Significance test for a proportion with review of confidence interval for a proportion 24 points 5. Inyour own words, summarize the results of your statistical analyses of the proportion of adults in the US who work for a government employer. This should include the following: d. b. C. d. ] Briefly describe the data and report descriptive statistics (sample size, sample proportion). State your null and alternative hypotheses. Describe results of the inferential statistics that you found, including the significance test (Z test for a proportion) and confidence interval. Report the Z statistic, P-value, and a-level (alpha level) that you used for your significance test. Your decision about the null hypothesis. Describe what the confidence interval shows about opinions. Provide a substantive conclusion about your findings (either change or stability) in the proportion of adults working for government, along with evidence to support that conclusion.

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