Sociology 272:

Making Sense of Sociological Data

**Problem Set 8**

Due Tuesday, November 17^{th} @ (noon)

Note that per the syllabus, assignments must adhere to the following guidelines to be considered for full credit:

- Be neat and organized
- Show work for ALL calculations and include SPSS output/tables for SPSS components
- Round decimal places appropriately (i.e., to 2 decimal places).
- Combine all problem set parts including calculations, work shown, and SPSS documentation, into a single PDF file that can be submitted to Dropbox.

Keep in mind that you may complete calculations by hand and scan them into a single PDF document to submit to Dropbox. If you decide to complete your problem set electronically, you must still be sure to show your work within the document to have your assignment considered for full credit.

**Notes specific to this Problem Set: **

To receive full credit for each of the problems listed below, you need to do the following:

- state the research and null hypotheses
- state the critical value
- calculate the test statistic
- make a decision to reject or fail to reject the null hypothesis
- interpret the results in a sentence or two

** Please also keep in mind that if the confidence level or alpha is not specified in the problem, you should assume a 95% confidence level (α=0.05).** Please note that the document entitled “Steps for Hypothesis Testing” has been posted to OAKS for your use on this problem set.

- The students at Smithville High School attend an average of 3.4 parties per month. A random sample of 219 seniors averages 3.9 parties per month, with a standard deviation of 0.37 parties. Are seniors significantly different from the student body as a whole in terms of the average number of parties they attend per month? (
*HINT: The wording of the research question suggests a two-tailed test. This means that the alternative, or research, hypothesis in step 2 will be stated as*. See your Z-distribution table*and that the critical region will be split between the upper and lower tails of the sampling distribution**for values of Z(critical) for various alpha levels.)* - What if the research question were changed to “Do seniors attend a significantly
number of parties, on average, than the whole student body”? How would the test conducted in part A change? Be specific in your response by showing differences that may emerge in*greater*of the hypothesis test. (*each step*part a,*HINT: This wording implies a one-tailed test of significance. How would the research hypothesis change? For the alpha you used in*)*what would the value of Z(critical) be? Would the test statistic change? Do you reject the null or fail to reject? Does the interpretation change? If yes, how so?*

- Across the city, seniors’ average score on the verbal portion of the SAT exam is 478, with a standard deviation of 18. A random sample of 147 seniors at Gifted High School has a mean score of 492. Is there a significant difference between the seniors at Gifted High and all of the seniors? Please conduct a hypothesis test to answer this question.
- A sample of 220 postal workers from Peoria, IL $30,000 per year. Imagine that the average salary for all Peoria workers is $32,225, with a standard deviation of $1443. Do postal workers make, on average, significantly less than Peoria workers on average? Please conduct a one- or two-tailed test to answer this question and explain your reasoning for selecting a one- or two-tailed test.

- Statewide, the population as a whole watches 14.7 hours of TV per day. A random sample of 200 college students in the state report watching an average of 14.3 hours per day, with a standard deviation of 1.2. Is there a significant difference between college students and the rest of the state’s population?