Exam 8: Hypothesis Testing for Population Proportions

List and verify that the conditions hold so that the sampling distribution of the z test statistic will approximately follow the standard normal distribution.

Complete the statement by filling in the blanks. A research hypothesis is always expressed in terms of ________ __________ because we are interested in making statements about the _________ based on _______ statistics.

[Objective: Interpret the parts of the hypothesis test] A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are . The test statistic and p-value for the test are z=-3.01 and p-value =0.0013. For a significance level of , choose the correct conclusion regarding the null hypothesis.

Check that the conditions hold so that the sampling distribution of the z-statistic will approximately follow the standard Normal distribution. Are the conditions satisfied? If not, choose the condition that is not satisfied.

Based on a 5% significance level, write a conclusion by interpreting the p- value. Be sure to clearly state the decision regarding the null hypothesis.

Which of the following is not one of the components of a hypothesis test?

The alternative hypothesis is a two-tailed with a z-score = −1.88

When a two-sample test of proportions is conducted, there are two conditions of independence that must be checked. State the two conditions of independence. Be sure that your statement clearly states the difference between the two conditions.

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. -Explain how you can determine the significance by using the calculated z-value.

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. -Calculate the z test statistic for the sample results. Round to the nearest hundredth.

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 describing the meaning of the level of significance in the context of the hypothesis test.

Read the following then choose the appropriate test and name the population(s). A researcher asks a random sample of 200 men whether they had made an online purchase in the last three months. He wants to determine whether the proportion of men who make online purchases is less than 0.18.

A researcher asks random samples of residents of two separate counties as to whether they had purchased organically grown food in the last three months. He wants to determine whether the proportion of residents of one county who purchase organically grown food is greater than the proportion of residents of the second county who purchase organically grown food. Choose the appropriate test and name the population(s).

[Objective: Test a hypothesis for a population proportion] Suppose a city official conducts a hypothesis test to test the claim that the majority of voters support a proposed tax to build sidewalks. Assume that all the conditions for proceeding with a one-sample test on proportions have been met. The calculated test statistic is approximately 1.40 with an associated p-value of approximately 0.081. Choose the conclusion that provides the best interpretation for the p-value at a significance level of

Which statement best describes the significance level of a hypothesis test?

A research firm carried out a hypothesis test on a population proportion using a left-tailed alternative hypothesis. Which of the following z-scores would be associated with a p-value of 0.025? Round to the nearest hundredth.

A researcher believes that children who attend elementary school in a rural setting have lower obesity rates then children who attend elementary school in an urban setting. The researcher collects a random sample from each population and records the proportion of children in each sample who were clinically obese. The data are summarized in the table below. Assume all the conditions for proceeding with a two-sample test have been met. Find the z-statistic (rounded to the nearest hundredth) and p-value (rounded to the nearest thousandth) for this hypothesis test. Using a 5% significance level, state the correct conclusion regarding the null hypothesis

Explain why failing to reject the null hypothesis does not prove that the null hypothesis is true.

[Objective: Understand the hypothesis test of proportions from two populations] A researcher believes that the exercise habits of men and women are different. He takes a random sample from each population and records the response to the question, "Did you exercise for at least 30 minutes twice a week?" The null hypothesis is Choose the correct alternative hypothesis.