Exam 8: Hypothesis Testing for Population Proportions

[Objective: Understand the components of hypothesis testing] Complete the statement by filling in the blanks. The null hypothesis H₀ is the statement of and always has a hypothesis. It is a statement about the hypothesis H₂ is the of a hypothesis. It is a statement about the value of a ___ that we intend to test.

The worker at a carnival game claims that he can communicate with a small magic rock and to prove it he tells you to hide it in your hand behind your back and he will identify the hand holding the rock. Being a wise student of statistics, you decide to stand back and observe the outcome of the next ten games before deciding whether to pay your three dollars to play the game. You have just conducted an informal hypothesis test. State the null and alternative hypothesis.

[Objective: Understand the components of hypothesis testing] Read the following problem description then choose the correct null and alternative hypothesis: A new drug is being tested to see whether it can reduce the rate of food-related allergic reactions in children ages 1 to 3 with food allergies. The rate of allergic reactions in the population of concern is 0.03 .

A polling agency is interested in testing whether the proportion of women who support a female candidate for office is less than the proportion of men. The null hypothesis is that there is no difference in the proportions of men and women who support the female candidate. The alternative hypothesis is that the proportion of women who support the female candidate is less than the proportion of men. The test results in a p-value of 0.041. Which of the following is the best interpretation of the p-value?

Choose the statement that best describes the significance level in the context of the hypothesis test.

From the TI-84 graphing calculator screenshots below, choose the screenshot whose shaded area correctly depicts the following hypothesis test results:

Which of the following is not a condition that must be checked before proceeding with a two-sample test?

[Objective: Calculate the observed value of the z-statistic from sample data] Suppose that the following is to be tested: and Calculate the observed z-statistic for the following sample data: Sixty-eight out of ninety test subjects have the characteristic of interest. Round to the nearest thousandth.

A polling agency is interested in testing whether the proportion of women who support a female candidate for office is greater than the proportion of men. The null hypothesis is that there is no difference in the proportion of men and women who support the female candidate. The alternative hypothesis is that the proportion of women who support the female candidate is greater than the proportion of men. The test results in a p-value of 0.112. Which of the following is the best interpretation of the p-value?

[Objective: Calculate the observed value of the \mathrm{z}-statistic from sample data] Two researchers are comparing a blood pressure reducing drug with a two-sided altemative hypothesis. Their test statistics show that the following z values: Which one of these have the smaller p-value and why?

For the following description, state whether a one- proportion z-test or a two-proportion z-test would be appropriate, and name the population. A researcher asks people who are 20-29 years old and senior citizens (people over 65) whether they support a new tax on income. He wants to determine whether the proportions that support the tax differ for these age groups.

[Objective: Understand the hypothesis test of proportions from two populations] A researcher believes that the proportion of women that exercise with a friend is greater than the proportion men. He takes a random sample from each population and records the response to the question, "Have you exercised with a friend at least once in the last seven days?" The null hypothesis is Choose the correct altemative hypothesis.

[Objective: Understand the p-value] From the TI-84 graphing calculator screenshots below, there are specific shaded areas that represent p-values. Choose the statement that best describes the interpretation of these p-values.

A sociologist believes that families that eat at least one meal a day together (without the interference of any other media) will have better communication skills. The sociologist conducts a study to see if there is a difference in the proportion of meals that are eaten together as a family for families living in a rural setting compared to families living in an urban setting.She collects a random sample from each population and records the proportion of test subjects that reported that they had eaten at least 3 meals per week together as a family. The data are summarized in the table below. Assume the all conditions for proceeding with a two-sample test have been met.

Use the following information to answer questions (10)- (12). A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are the same as the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest. - [Objective: Test a hypothesis for a population proportion] A researcher completes a hypothesis test with a resulting p-value = 0.076. Choose the best statement to interpret the results

Which of the following is not true about the alternative hypothesis?

Use the following information to answer questions (3) - (7). A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test whether the claim is true or not, a random sample of 100 doctors is obtained. Of these doctors, 82 indicated that they recommend aspirin for headaches. Is the claim accurate? Test with a significance level of 0.05. -Write a statement explaining what the p-value means and how it should be interpreted. For questions (8) and (9), shade the approximate area that would represent the p-value for the alternative hypothesis and z-score, and then calculate the p-value. Round to the nearest thousandth.

Read the following problem description then choose the correct null and alternative hypothesis. A new drug is being tested to see whether it can reduce the diastolic blood pressure measurement for adults age 45-60 years. The upper limit for diastolic blood pressure measurement should be 90 mmHg.

The alternative hypothesis is a right-tailed with a z-score = 0.21