Exam 12: Testing Hypotheses About Proportions

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. -For a significance level of $\alpha$ = 0.05, are the results statistically significant?

A drug shows promise as a new treatment for hay fever. The hypotheses below were tested for p = proportion of patients taking this drug who are cured of hay fever. H₀: p ≤ 0.80 H_a: p >0.80 What are the Type 1 and Type 2 errors for this study?

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 this hypothesis test. -z-statistic = -1.50. p-value = ?

Use the following information for questions: A university administrator writes a report in which he states that at least 45% of all students have driven while under the influence of drugs or alcohol. Many others think the correct percent is less than 45%. -To resolve the issue, a random sample of 400 students is obtained and it is found that 156 or 39% admit that they have driven under the influence of drugs or alcohol. Here is some Minitab output: What conclusion should be made?

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. -State your conclusion.

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? -Using a 5% significance level, does there appear to be a majority of people in the population who favor banning handguns?

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

If, in a hypothesis test, the null hypothesis is actually true, which type of mistake can be made?

A hypothesis test gives a p-value of 0.03. If the significance level $\alpha$ = 0.05, the results are said to be

Use the following information for questions: Time magazine recently polled 500 13-year-olds online to get a glimpse into their world. The results may surprise many people: 13-year-olds in 2005 enjoy their relationships with their parents, are less likely to drink or do drugs than previous generations, and they are highly focused, competitive and determined to succeed. The overscheduled toddlers of the 1990s are now controlling their own schedules, and in many cases, their days are just as jam-packed as ever. It seems today's teens are not only used to being extremely busy, they thrive on it. One result from the Time Poll was that 53 percent of the 13-year-olds polled said their parents are very involved in their lives. Suppose that 200 of the 13-year olds were boys and 300 of them were girls. We wish to find out if the proportion of 13-year old boys and girls who say that their parents are very involved in their lives are the same. Let the boys be represented by subscript 1 and girls by 2. -What is the numerical value of the p-value for this test?

A z-test to compare two population proportions is to be conducted. One condition for this z-test to be valid is that both populations have Normal distributions.

In an American criminal trial, the null hypothesis is that the defendant is innocent and the alternative hypothesis is that the defendant is guilty. Which of the following describes a Type 2 error for a criminal trial?

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 the study gave a p-value of 0.01. What is the decision?

Use the following information for questions: A university administrator writes a report in which he states that at least 45% of all students have driven while under the influence of drugs or alcohol. Many others think the correct percent is less than 45%. -Which of the following statements describes the p-value that was calculated in this situation?

Which one of the following is not true about hypothesis tests?

In hypothesis testing for one proportion, the "null value"is used in which of the following?

About 90% of the general population is right-handed. A researcher speculates that artists are less likely to be right-handed than the general population. In a random sample of 100 artists, 83 are right-handed. Which of the following best describes the p-value for this 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 = 2.00. p-value = ?

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 = 0.40. p-value = ?

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 overweight men is greater than the proportion of overweight women in America.