Exam 12: Testing Hypotheses About Proportions

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 500 trees in the park, is the difference between the observed percentage of 7% and the hypothesized value of 5% statistically significant (use $\alpha$ = 0.05)?

Use the following information for questions: Data were collected by giving a survey to a random sample of students at a university. One question asked was: "Do you believe in extraterrestrial life?"Here is a comparison of the proportions of males and females that said "yes": Subscripts in these questions are 1 = females, 2 = males. -Suppose we wish to know if females at the university are less likely to believe in extraterrestrial life than males. What are the appropriate null and alternative hypotheses?

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 price of a particular statistics textbook over the internet is the same as the average price of the textbook sold at all bookstores in a college town.

Use the following information for questions: Data were collected by giving a survey to a random sample of students at a university. One question asked was: "Do you believe in extraterrestrial life?"Here is a comparison of the proportions of males and females that said "yes": Subscripts in these questions are 1 = females, 2 = males. -Is there statistically significant evidence that females are less likely than males to believe in extraterrestrial life?

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 sample proportion of people who favor banning handguns? Include the appropriate symbol in your answer that represents this value.

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 value of 10% was obtained ten years ago. The alternative hypothesis will state that the proportion of students who own their own car has increased from the value ten years ago. What is the alternative hypothesis for p?

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 -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 = 0.70 H_a: p ≠ 0.70 For each z-statistic, calculate the p-value for the hypothesis test. -z-statistic = -0.40. p-value = ?

Which of the following conclusions is not equivalent to rejecting the null hypothesis?

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

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 500 trees in the park, what is the value of the test statistic for testing these hypotheses and the corresponding 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 = 0.00. p-value = ?

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. -In the sample, 93 boys and 172 girls said that their parents are very involved in their lives. Under the null hypothesis, what is the numerical value of the estimate for the common population proportion of 13-year olds who say that their parents are very involved in their lives?

Use the following information for questions: A study was conducted to learn about drinking and driving habits of male and female college students. Independent random samples of 942 female students and 754 male students were obtained. Of those sampled, 181 female and 181 male students admitted that they had driven after consuming an alcoholic beverage. Is this sufficient evidence to conclude that male college students tend to drive after drinking more frequently than female college students? Let 1 = females and 2 = males, so that the appropriate hypotheses to be tested are:H₀: p₁ = p₂ versus H_a: p₁ < p₂. Set the significance level to 0.01. -Assuming the null hypothesis is true, what is the estimate of the common population proportion p?

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

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 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 ≥ 0.40 H_a: p < 0.40 For each z-statistic, calculate the p-value for this hypothesis test. -z-statistic = 0.50. p-value = ?

In hypothesis testing, a Type 2 error occurs when

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. -What distribution would have been used to find the exact p-value for the test regarding the population of all employees? Provide details to fully specify the distribution.

Which statement is correct about a p-value?