Exam 12: Testing Hypotheses About Proportions

The data summary used to decide between the null hypothesis and the alternative hypothesis is called a

Use the following information for questions: The null hypothesis for p = proportion of students who own their own car is H₀: p = 0.10. The significance level is set at $\alpha$ = 0.05. -The results of a study gave a p-value of 0.01. State your conclusion.

Use the following information for questions: An ESP experiment is done in which a participant guesses which of 4 cards the researcher has randomly picked, where each card is equally likely. This is repeated for 200 trials. The null hypothesis is that the subject is guessing, while the alternative is that the subject has ESP and can guess at higher than the chance rate. -Which of the following would be a Type 1 error in this situation?

Use the following information for questions: For each statement, determine if the statement is a typical null hypothesis $H_0$ or alternative hypothesis $H_a$ . -The proportion of second year college students who live in a dormitory has decreased from the proportion in 1999, which was known to be 25%.

Use the following information for questions: Suppose that two different studies were conducted to determine whether the proportion of overweight men is 30% (null hypothesis) or different from 30% (alternative hypothesis). One study enrolled 100 men, while the other study enrolled 1000 men. Both studies resulted in the same sample proportion of overweight men, 35%. However, the p-values were very different: one study gave a p-value = 0.275 while the other study gave a p-value = 0.0006. -Explain why the p-values are so different.

Use the following information for questions: A random sample of 800 high school boys showed that 420 had done strenuous exercise during the past year. The researcher wants to test the hypotheses below for p = the proportion of all high school boys who do strenuous exercise. H₀: p ≤ 0.50 H_a: p > 0.50 -State the null hypothesis (H₀) and the alternative hypothesis (H_a) in words.

Use the following information for questions: A random sample of 600 high school boys showed that 40 had taken diet pills during the past 30 days to lose weight The researcher wants to test the hypotheses below for p = the proportion of all high school boys who take diet pills to lose weight. H₀: p =0.10 H_a: p ≠ 0.10 -Verify necessary data conditions for a z-statistic and calculate the z-statistic.

Use the following information for questions: A random sample of 850 high school girls showed that 400 had done strenuous exercise over the past year. The researcher wants to test the hypotheses below for p = the proportion of all high school girls who do strenuous exercise. H₀: p ≥ 0.50 H_a: p < 0.50 -Are the results statistically significant at a significance level of $\alpha$ = 0.05?

Use the following information for questions: For each statement, determine if the statement is a typical null hypothesis $H_0$ or alternative hypothesis $H_a$ . -The graduation rate for all division I athletes is not equal to the 85% claimed by the NCAA.

Use the following information for questions: Gun control is a sensitive issue in the US. In a survey, 650 people favored a ban on handguns out of a total of 1250 individuals polled. Do the data provide sufficient evidence to conclude that a majority of individuals in the population favor banning handguns? -Could you have made a mistake when making your decision in question 104? If yes, what is this mistake called? If no, explain briefly why not.

Use the following information for questions: A random sample of 800 high school boys showed that 420 had done strenuous exercise during the past year. The researcher wants to test the hypotheses below for p = the proportion of all high school boys who do strenuous exercise. H₀: p ≤ 0.50 H_a: p > 0.50 -Verify necessary data conditions for a z-statistic and calculate the z-statistic.

Use the following information for questions: The null hypothesis for p = proportion of students who own their own car is H₀: p = 0.10. The significance level is set at $\alpha$ = 0.05. -Based on your decision in question 39, what mistake (error) could have been made?

A hypothesis test is done in which the alternative hypothesis states that more than 10% of a population is left-handed. The p-value for the test is calculated to be 0.25. Which statement is correct?

Use the following information for questions: Suppose a park ranger wishes to collect some data from the State Park he works in to asses if the proportion of trees in the park that are in need of pruning is significantly higher than 5%. He will test the hypotheses H₀: p = 0.05 vs. H_a: p > 0.05. After a week of hard work, randomly selecting and inspecting trees throughout the entire park, the park ranger found that 7% of the trees in the sample were in need of pruning. -Explain in your own words why the results of the test were so different, even though the sample proportion was 7% in both cases.

Use the following information for questions: An airport official wants to prove that the p₁ = proportion of delayed flights after a storm for Airline A is less than p₂ = the proportion of delayed flights for Airline B. Random samples from two airlines after a storm showed that 51 out of 200 of Airline A's flights were delayed, and 60 out of 200 of Airline B's flights were delayed. -What is the p-value? (computer or calculator for normal distribution required)

Use the following information for questions: Suppose a park ranger wishes to collect some data from the State Park he works in to asses if the proportion of trees in the park that are in need of pruning is significantly higher than 5%. He will test the hypotheses H₀: p = 0.05 vs. H_a: p > 0.05. After a week of hard work, randomly selecting and inspecting trees throughout the entire park, the park ranger found that 7% of the trees in the sample were in need of pruning. -Think about the park ranger's job when answering the following question. Is the difference between the observed percentage of 7% and the hypothesized value of 5% practically significant?

In hypothesis testing, a Type 1 error occurs when

Use the following information for questions: For each statement, determine if the statement is a typical null hypothesis $H_0$ or alternative hypothesis $H_a$ . -There is no difference between the proportion of overweight men and overweight women in America.

Use the following information for questions: A random sample of 850 high school girls showed that 400 had done strenuous exercise over the past year. The researcher wants to test the hypotheses below for p = the proportion of all high school girls who do strenuous exercise. H₀: p ≥ 0.50 H_a: p < 0.50 -Find the p-value.