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Hypothesis Testing Activity
Posted:
Mar 13, 1997 6:41 AM


Hello All,
As we finish our study of hypothesis testing and confidence intervals in my AP Stats class, I would like to ask the students to complete the following exercise. I would ask your counsel for this same task before I put it to the kids.
The instruction was to indicate the ÃÂmost appropriateÃÂ test (if any) for each part of each scenario. Students were asked to identify the test, the null and alternative hypotheses, and to justify their choice.
1. A manufacturer claims mean life of 39.5 hours with a standard deviation of 4.5 hours for his product. You run a simple random sample to test this claim. a) a sample of 10 has a mean of 37.0 hours and a standard deviation of 2.5 hours. b) a sample of 50 has a mean of 37.0 hours and a standard deviation of 2.5 hours.
2. An advertiser claims that 80% of the adult population chooses their product over the product of their closest competitor. A simple random sample of adult consumers is conducted. a) a sample of 25 indicate that only 60% would choose the product in question. b) a sample of 100 indicate that only 60% would choose the product in question.
3. One of your peers claims that boys are smarter than girls in math classes. Together you run two simple random samples and calculate the given summary statistics of the boys and the girls for comparable math classes. a) in Calculus, 15 boys had a mean of 82.3 with st. dev. of 5.6; 12 girls had a mean of 81.2 with st. dev. of 6.7. b) in Algebra 2, 40 boys had a mean of 73.4 with st. dev. 10.9; 50 girls had a mean of 75.4 with a st. dev. of 9.8. c) in 8th grade math, 20 boys had a mean of 78.6 with a st. dev. of 6.7; 35 girls had a mean of 77.3 with a st. dev of 7.5.
4. An experiment is developed to test the effectiveness of a new fertilizer for plant growth. Randomly selected shoots are placed either in a control flat or in a treatment flat. The control flat is subjected to water only; while the treatment flat is given water and the new fertilizer. The percent of growth after three weeks for each group is computed and the mean proportion of growth is reported. a) 16 plants in the control flat had a mean proportion of .78; 16 plants in the treatment flat had a mean proportion of .83. b) 16 plants in the control flat had a mean proportion of .78; 30 plants in the treatment flat had a mean proportion of .83. c) 100 plants in the control flat had a mean proportion of .78; 50 plants in the treatment flat had a mean proportion of .83.
5. It is known that student performance on each SAT test follows a normal distribution. At a particular school, a principal chooses to study whether her students perform better on the Math section or the Verbal section of the test. a) She chooses a simple random sample of students whose scores are known. She subtracts the Math score  Verbal score and computes that the mean difference in the scores is 23.3 with a st. dev. of 10.1. b) She chooses a simple random sample of students whose scores are known. She computes the mean Math performance of the students to be 524.5 with a st. dev. of 35.4 and the mean Verbal performance of the students to be 517.5 with a st. dev. of 42.3. c) She chooses two independent random samples of students whose scores are known. She computes the mean Math performance of one of the samples to be 524.5 with a st. dev. of 35.4 and the mean Verbal performance of the other sample to be 517.5 with a st. dev. of 42.3. d) She takes all of the scores of her students and calculates the differences between their Math and Verbal scores to be 23.3 with a st. dev. of 10.1. e) She takes all of the scores of her students and calculates the mean Math performance to be 524.5 with a st. dev. of 35.4 and the mean Verbal performance to be 517.5 with a st. dev. of 42.3.
Thanks in advance. I am most interested in 1. Do you agree that this is valuable exercise? 2. If so, your answers would be helpful. You need only indicate an appropriate test. 3. Any suggestions to improve this activity. Did I miss any scenarios with which the kids should grapple?
Jim Bohan Manheim Township School District Lancaster PA 17601



