Exam 12: Testing Hypotheses About Proportions

Use the following information for questions: A sample of n = 200 college students is asked if they believe in extraterrestrial life and 120 of these students say that they do. The data are used to test H₀: p = 0.5 versus H_a: p > 0.5, where p is the population proportion of college students who say they believe in extraterrestrial life. The following Minitab output was obtained: -What is the correct description of the area that equals the p-value for this problem?

Use the following information for questions: An airport official wants to prove that the p₁ = proportion of delayed flights after a storm for Airline 1 was different from p₂ = the proportion of delayed flights for Airline 2. Random samples from the two airlines after a storm showed that 50 out of 100 of Airline 1's flights were delayed, and 70 out of 200 of Airline 2's flights were delayed. -What are the appropriate null and alternative hypotheses?

Use the following information for questions: A hypothesis test for a population proportion p is given below: H₀: p = 0.70 H_a: p ≠ 0.70 For each z-statistic, calculate the p-value for the hypothesis test. -z-statistic = 0.50. p-value = ?

Use the following information for questions: Suppose the significance level for a hypothesis test is $\alpha$ = 0.05. -If the p-value is 0.001, the conclusion is to

Which of the following is not a valid conclusion for a hypothesis test?

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 -Report the conclusion in the context of the situation.

Use the following information for questions: A hypothesis test for a population proportion p is given below: H₀: p ≤ 0.40 H_a: p > 0.40 For each z-statistic, calculate the p-value for the hypothesis test. -z-statistic = 0.50. p-value = ?

The smaller the p-value, the

The p-value for a one-sided test for a population proportion was 0.02. The p-value for the corresponding two-sided test would be:

Use the following information for questions: The null and alternative hypotheses for p = proportion of students who buy at least 3 textbooks in a semester is given below: H₀: p = 0.80 (or p ≤ 0.80) H_a: p > 0.80 The results of a study gave a p-value of 0.08. The results of this study also stated that the study results were not statistically significant. -Give an example of a significance level the researchers performing the study could have used.

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? -State the appropriate hypotheses about p, the population proportion of people who favor banning handguns.

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? -What is the numerical value of the corresponding p-value?

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. -The subject actually gets 70 correct answers. Which of the following describes the probability represented by the p-value for this test?

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. -If the park ranger collected data on 100 trees in the park, what is the value of the test statistic for testing these hypotheses and the corresponding p-value?

A null hypothesis is that the probability is 0.7 that a new drug will provide relief in a randomly selected patient. The alternative is that the probability of relief is greater than 0.7. Suppose the treatment is used on 500 patients and there are 380 successes. How would a p-value be calculated in this situation?

Use the following information for questions: Let p represent the population proportion of all employees at a large company who are "very concerned"or "somewhat concerned"about having the money to make their monthly mortgage or rent payment. A local organization would like to assess at a 10% significance level if a majority of all employees are worried about making their mortgage or rent payments, namely, H₀: p = 0.50 versus H_a: p > 0.50. A random sample of 20 such employees yields just 8 adults who say they are "very concerned"or "somewhat concerned"about having the money to make their monthly payment. -Without actually computing it, will the resulting p-value be less than 0.50, equal to 0.50, or more than 0.50?

Past data indicates an 80% (0.8) success rate in treating a certain medical problem. A new treatment is used on 100 patients in a clinical trial. It is successful in 87% (0.87) of the cases. What is the value of the z-score that can be used to test the null hypothesis that the success rate is 80%?

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 -Find the p-value.

Explain what the statement of the null hypothesis represents in hypothesis testing. Give an example.

Null and alternative hypotheses are statements about