Hypothesis testing of a single mean and/or single proportion

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(Comment.gif: This is an activity resource. It would be better located as a subpage of a main page about hypothesis testing. --Alison Snieckus 21:06, 25 March 2010 (UTC))

This activity offers students direct experience with the 4 steps involved in hypothesis testing for the population proportion or 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.[1]

Hypothesis testing activity

Estimate for completion time: 60 minutes spread over two meetings, with data collection occurring between meetings

Materials needed:

  • Access to desired sample (face-to-face, cell phone, ...)
  • Spreadsheet software (Excel or Calc)



Icon activity.jpg

Activity

Hypothesis Testing Scenarios

Scenario 1: Television Survey

In a 2009 Nielsen survey, it was stated that Americans (2 years and older) watch television on average 35 hours per week.[2] It seems likely that high school and college students don't watch nearly this much television per week. Identify a random (or pseudo-random) sample and conduct a hypothesis test to determine if indeed the average for high school and college students is lower.

Scenario 2: Language Survey

According to the 2000 US Census, about 39.5% of Californians, 25.5% of New Jerseyans and 17.9% of all Americans speak a language other than English at home.[3] Depending on the state, the percentage may have increased or decreased. Identify a random (or pseudo-random) sample and conduct a hypothesis test to determine if the percent of people in your state that speak a language other than English at home is different from the percentage reported in the 2000 census.

Scenario 3: Jeans Survey

Cotton Incorporated reported in March 2010 that 13-24 year old females own on average 9 pairs of jeans.[4] This number seems high (after all it's a marketing publication). Identify a random (or pseudo-random) sample of 13-24 year old females and conduct a hypothesis test to determine if the average number of jeans owned is less than 9.

Scenario 4: Sleep Survey

In a 2006 survey by the National Sleep Foundation, US high school students were found to get an average of 7.2 hours of sleep per night.[5] Experts indicate that high school students need 9 hours of sleep per night. It is thought that early school start times contribute to the lack of sleep for many students. Do high school students who do not attend a public or private high school (that is, are homeschooled) sleep more than 7.2 hours per night? Identify a random (or pseudo random sample of homeschooled high school students and conduct a hypothesis test to determine if the average number of hours of sleep is more than 7.2.


Design and implement hypothesis test(s)

Design and implement the study for one or more of the scenarios (alternatively, devise your own scenario). For each study:

  1. 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 or P-hat, represents.
    • State what test statistic will be used to summarize the data.
  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.
    • Calculate summary statistics and a histogram (if appropriate) based on the sample data.
    • Confirm that the conditions for use of the chosen test statistic have been met.
    • Calculate the test statistic.
  3. Find the p-value of the test.
    • 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
  4. 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.


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/.

References

  1. ↑ Open Learning Initiative. Statistics. Retrieved from the Open Learning Initiative web site http://oli.web.cmu.edu/openlearning/forstudents/freecourses/statistics.
  2. ↑ Nielsen Three Screen Report, 4th quarter 2009
  3. ↑ [http://www.census.gov/prod/2003pubs/c2kbr-29.pdf Language Use and English-Speaking Ability: 2000], issued in October 2003. Table 2, p. 5.
  4. ↑ The Skinny (and Straight) on Jeans
  5. ↑ 2006 Sleep in America Poll: Summary of Findings, p. 7.
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