Exam 12: Testing Hypotheses About Proportions

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 average time to graduate for undergraduate English majors is less than the average time to graduate for undergraduate history majors.

The p-value for a two-sided test for a population proportion was 0.04. The p-value for a one-sided test would be:

A z-test to compare two population proportions is to be conducted. One condition for this z-test to be valid is that both samples sizes are large.

Use the following information for questions: A hypothesis test for a population proportion p is given below: H₀: p = 0.10 H_a: p ≠ 0.10 For each sample size n and sample proportion $\hat{p}$ compute the value of the z-statistic. -Sample size n = 500 and sample proportion $\hat{p}$ = 0.20. z-statistic = ?

A z-test for testing hypotheses about a population proportion is to be conducted.One condition for this z-test to be valid is that the sample size is adequately large enough.

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 is the p-value? (computer or calculator for normal distribution required)

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 = 0.00. p-value = ?

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 = 2.00. p-value = ?

When the p-value is less than or equal to the designated level of 0.05, the result is called a

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. -Is the probability that we have made a Type 1 error equal to 1% (0.01)?

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 -Are the results statistically significant at a significance level of $\alpha$ = 0.05?

Use the following information for questions: Suppose the significance level for a hypothesis test is $\alpha$ = 0.05. -If the p-value is 0.049, the conclusion is to

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%. -What are appropriate null and alternative hypothesis in this situation?

Use the following information for questions: Suppose the significance level for a hypothesis test is $\alpha$ = 0.05. -If the p-value is 0.999, the conclusion is to

Use the following information for questions: A hypothesis test for a population proportion p is given below: H₀: p = 0.10 H_a: p ≠ 0.10 For each sample size n and sample proportion $\hat{p}$ compute the value of the z-statistic. -Sample size n = 500 and sample proportion $\hat{p}$ = 0.04. z-statistic = ?

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 -Are the results statistically significant at a significance level of $\alpha$ = 0.05?

Suppose a 95% confidence interval for p, the proportion of drivers who admit that they sometimes run red lights when no one is around, is 0.29 to 0.38. Which of the following statements is false?

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. -Are the data statistically significant that the 1% significance level?

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. -Calculate the value of the test statistic.

A z-test for testing hypotheses about a population proportion is to be conducted. One condition for this z-test to be valid is that the population of all responses has a Normal distribution.