Groupwork06

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Jan 9, 2024

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Math 10 Hypothesis Testing 2 1. A researcher wants to support the claim that students spend less than 7 hours per week doing homework. The sample size for the test is 64 students. The drawing is a diagram of a hypothesis test for population mean under the Null Hypothesis (top drawing) and under the Alternative Hypothesis (bottom drawing). a. State the Null and Alternative Hypotheses. b. What is the design probability associated with Type I error? c. What is the design probability associated with Type II error? d. What is the power of the test shown in this graph? e. If the p-value of the test came out to be .08, what would the decision be? Also, write the conclusion in the context of the problem f. What is the value of the mean under the Alternative Hypothesis? g. What is the effect size of this test? Explain what it means . h. If the sample size was changed to 100, would the shaded area on the bottom graph increase, decrease or stay the same?

2. An environmentalist estimates that the mean waste recycled by adults in the United States is more than 1 pound per person per day. You want to support this claim. You find that the mean waste recycled per person per day for a random sample of 12 adults in the United States is 1.2 pounds and the sample standard deviation is 0.3 pound. At α = 0.05, can you support the claim? (DESIGN) State your Hypothesis in words and population parameters (DESIGN) State Significance Level of the test and explain what Type I error would be. (DESIGN) Determine the statistical model (test statistic) (DESIGN) Determine decision rule (p-value method) (DATA) Conduct the test by calculating the test statistic and p-value using the p-value calculator . Paste graph here. State your decision: reject or fail to reject Ho (CONCLUSION) State your overall conclusion in language that is clear, relates to the original problem and is consistent with your decision.

3. A government association claims that 44% of adults in the United States do volunteer work. You work for a volunteer organization and are asked to test this claim. You find that in a random sample of 1165 adults, 556 do volunteer work. At α = 0.05, do you have enough evidence to reject the association's claim? (DESIGN) State your Hypothesis in words and population parameters (DESIGN) State Significance Level of the test and explain what Type II error would be. (DESIGN) Determine the statistical model (test statistic) (DESIGN) Determine decision rule (p-value method) (DATA) Conduct the test by calculating the test statistic and p-value using the p-value calculator . Paste graph here. State your decision: reject or fail to reject Ho (CONCLUSION) State your overall conclusion in language that is clear, relates to the original problem and is consistent with your decision.

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4. This exercise shows the significance level of a test (α ) and the p-value do not tell you the confidence of your claim being correct if you reject Ho. α = P(Reject Ho | Ho is true) power = P(Reject Ho | Ho is False) A researcher wanted to show that the percentage of students at community colleges who receive financial aid exceeds 40%. Ho: p = 0.40 (The proportion of community college students receiving financial aid is 0.40) Ha: p > 0.40 (The proportion of community college students receiving financial aid is over 0.40) The researcher sampled 874 students and found that 376 of them received financial aid. This works to a sample proportion , which leads to a Z value of 1.822, if p = 0.40. p-value = P(> 0.430 | Ho is true) = P( Z > 1.822 ) = 0.034 a. The researcher then incorrectly claimed that “We are 96.6% confident that more than 40% of community colleges receive financial aid.” Explain why this is incorrect reasoning. For this researcher, suppose there is a 10% chance (without data) that Ha is True (meaning Ho is False). Let’s also assume the test has 85% power and that α = 0.05. We can now calculate the actual chance Ha is true given this data. We will use Bayesian Statistics, similar to the drug testing example of Chapter 4, to determine the probability that Ha will be true if you reject Ho. b. First complete the tree diagram. (double click into drawing and fill in the probabilities

c. Then create a hypothetical two-way table based on these probabilities. Ho is False Ha is True Ho is True Ho is False Total Reject Ho Fail to Reject Ho Total 100 900 1000 d. What is the probability that a researcher will reject Ho? e. If a researcher rejects Ho, what is the chance that Ho is really true? f. Why does this answer differ from the significance level (α )?

Groupwork06

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