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Exam 12: Testing Hypotheses About Proportions

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Question 21

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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 observed test statistic?

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Question 22

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The level of significance (usually .05) associated with a significance test is the probability

A) that the null hypothesis is true.
B) that the alternative hypothesis is true.
C) of not rejecting a true null hypothesis.
D) of rejecting a true null hypothesis.

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Question 23

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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, 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: 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 = -1.00. p-value = ?

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 value of the test statistic?

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. -What is the correct statement of the null hypothesis that the person does not have ESP?

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 = 100 and sample proportion $\hat{p}$ = 0.10. z-statistic = ?

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: -Using a 5% significance level, what is the correct decision for this significance test?

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 -Find the p-value.

A two-sided or two-tailed hypothesis test is one in which

Consider testing the alternative hypothesis that the proportion of adult Canadians opposed to same-sex marriage in Canada is less than 0.5. The test was conducted based on a poll of n = 1003 adults and it had a p-value of 0.102. Which of the following describes the probability represented by the p-value for this test?

Use the following information for questions: A researcher examined the folklore that women can predict the sex of their unborn child better than chance would suggest. She asked 104 pregnant women to predict the sex of their unborn child, and 57 guessed correctly. Using these data, the researcher created the following Minitab output. -Based on the information in the output, what is the appropriate conclusion the researcher can make about p = proportion of pregnant women who can correctly predict the sex of their unborn child?

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: -Suppose that the alternative hypothesis had been H_a: p ? 0.5. What would have been the p-value of the test?

A hypothesis test gives a p-value of 0.050. If the significance level $\alpha$ = 0.05, the results are said to be

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. -Report your conclusion in terms of the two airlines.

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: -Using a 5% significance level, what is the correct conclusion for this significance test?

Explain what is meant by the power of a hypothesis test and suggest one way a researcher might change their study design to increase the power of the test.

In a hypothesis test which of the following can (and should) be determined before collecting data?

In a hypothesis test the decision was made to not reject the null hypothesis. Which type of mistake could have been made?

The likelihood that a statistic would be as extreme or more extreme than what was observed is called a