Hypothesis testing of a single mean--hrs/wk watching tv

This activity offers students direct experience with the 4 steps involved in hypothesis testing for the population mean:

1. State the appropriate null and alternative hypotheses, Ho and Ha.
2. Obtain a random sample, collect relevant data, and check whether the data meet the conditions under which the test can be used. If the conditions are met, summarize the data by a test statistic.
3. Find the p-value of the test.
4. Based on the p-value, decide whether or not the results are significant and draw your conclusions in context.

Inference for the mean of a population

Use this activity for in-class collaborative group work.

Estimate for completion time: 45 minutes, with data collection occurring as students arrive for class.

Materials needed:

• 4-step hypothesis testing template (shown below) for each group (handout, in .odt file format--OpenOffice.org Writer)
• Analysis software (SPSS, PPSP, SAS, R, Minitab, Excel, Calc)

Activity

Testing the mean # of tv hours watched The 1st quarter 2010 Nielsen survey concludes that Americans (2 years and older) watch television on average 35.57 hours per week. It seems likely that graduate students (or pick some other sub-group) do not watch nearly this much television per week. Use your class as a sample; collect from each student his/her estimated number of hours of television watched per week. Summarize the sample data and test the sample mean against the given population mean. Data collection As students arrive for class, have them anonymously respond to the following question, by writing their response on a slip of paper. When data collection is complete, list each of the responses on the board, along with an ID number. "Generally speaking, how many hours per week do you watch tv?" Design and implement hypothesis test(s) Form students into groups of 2-4 students. Each group will need access to a laptop with statistical software loaded and a copy of the handout. Have the students complete the handout as a group, which includes the following information. State the appropriate null and alternative hypotheses and set the significance level. Ho: Ha: Significance level: In words, clearly state what your random variable, X-bar, represents. State what test statistic, and whether one-tailed or two-tailed, will be used to summarize the data. Use the collected class data as your sample. Check whether the data meet the conditions under which the test can be used. If the conditions are met, summarize the data by a test statistic. Calculate summary statistics and create a histogram (or stemplot) based on the sample data. Confirm that the conditions for use of the chosen test statistic have been met. (Continue even if conditions not met, and be ready to discuss noted violations in follow-up.) Calculate the test statistic. Find the p-value of the test. p-value: Explain what the p-value means. On a sketch of the normal distribution, label the x axis and shade the region(s) corresponding to the p-value Based on the p-value, decide whether or not the results are significant and draw your conclusions in context. Indicate whether or not Ho is rejected. Provide a reason for this decision. Draw conclusions based on the results, given the context of the scenario. If Ho is rejected, create a confidence interval appropriate to the given significance level. Follow-up discussion Review the results. Were the conditions met? Were the test results significant? What can we conclude about our research question based on the results. Are there limitations to our study? Sample -- do the students in our class represent a random sample? Size of sample -- if small, discuss implications (lack of power, impact of non-Normal population) Survey question -- are there ambiguities? how might these impact results? other limitations?

Resources

The following resources were used for ideas and organization in the development of this activity:

• Dean, S., & Illowsky, B. (2009, February 18). Hypothesis Testing of Single Mean and Single Proportion: Lab. Retrieved from the Connexions Web site: http://cnx.org/content/m17007/1.9/.