Exam 8: Hypothesis Testing for Population Proportions

Suppose a city official conducts a hypothesis test to test the claim that the majority of voters oppose a proposed school tax. Assume that all the conditions for proceeding with a one-sample test on Proportions have been met. The calculated test statistic is approximately 1.46 with an associated P-value of approximately 0.072. Choose the conclusion that provides the best interpretation for the P-value at a significance level of $\alpha = 0.05$

Use the following information to answer the question. A manager at a large office supply store believes that her supply of pencils has a defect rate that is higher than the defect rate stated by the manufacturer. The manager's null hypothesis is that the supply of pencils has a defect rate of $p = 0.025$ (the pencil manufacturer's stated defect rate). Suppose we do a test with a significance level of $0.05$ . Symbolically, the null and alternative hypothesis are as follows: $\mathrm { H } _ { 0 } : \mathrm { p } = 0.025$ and -The store manager calculates a p-value for the hypothesis test of 0.0030. Write a statementexplaining what the p-value means and how it should be interpreted.

Assuming the conditions for a two proportion z-test hold, state the alternative hypothesisthen find the observed test statistic and p-value. State your decision regarding the nullhypothesis,H0: p1=p2 $\mathrm { H } _ { 0 } : \mathrm { p } _ { 1 } = \mathrm { p } _ { 2 }$ . How do the test results compare to the expectations of the psychologist? Round to the nearest hundredth.

A polling agency is interested in testing whether the proportion of women who support a femalecandidate for office is greater than the proportion of men. The null hypothesis is that there is nodifference in the proportion of men and women who support the female candidate. The alternativehypothesis is that the proportion of women who support the female candidate is greater than theproportion of men. The test results in a p-value of 0.112. Which of the following is the bestinterpretation of the p-value?

Which statement best describes the power of a hypothesis test?

To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "blue collar" jobs to see whether their drinking habits are in the same proportion as the general public. The null hypothesis for this test is $\mathrm { H } _ { 0 } : \mathrm { p } = 0.26$ and the alternative hypothesis is $\mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.26$ . The researcher collected data from a random sample of 90 adults with "blue collar" jobs of which 30 stated that they drank once a week or less in the last month. Assume that the conditions that must be met in order for us to use the $\mathrm { N } ( 0,1 )$ distribution as the sampling distribution are satisfied. Find the values of the sample proportion, $\hat { p }$ , the test statistic, and the p-value associated with the test statistic. Round all values to the nearest thousandth.

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

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 $0.04$ ? Round to the nearest hundredth.

Use the following information to answer the question. A health foods shop owner is wondering if his customer's daily vitamin supplement habits are in the same proportion as the general population of adults. The shop owner heard in a news report that 60% of all adults reported that they took a daily vitamin. The shop owner believes that his customers have a greater proportion of adults who take a daily vitamin, so he decides to conduct a hypothesis test using the following null and alternative hypothesis: $\mathrm { H } _ { 0 } : \mathrm { p } = 0.6 \text { and } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.6$ e shop owner collected data from 50 randomly selected customers. -Based on a 5% significance level, write a conclusion by interpreting the p-value. Be sure toclearly state the decision regarding the null hypothesis.

A polling agency is interested in testing whether the proportion of women who support a femalecandidate for office is less than the proportion of men. The null hypothesis is that there is nodifference in the proportions of men and women who support the female candidate. The alternativehypothesis is that the proportion of women who support the female candidate is less than theproportion of men. The test results in a p-value of 0.041. Which of the following is the bestinterpretation of the p-value?

The janitor calculates a p-value for the hypothesis test of approximately 0.087. Choose the correct interpretation for the p-value.

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 $\mathrm { H } _ { 0 }$ : $\mathrm { p } _ { \text {women } } = \mathrm { p } _ { \text {men } }$ . Choose the correct alternative hypothesis.

Suppose the janitor tests 300 light bulbs and finds that 33 bulbs are defective. What value of the test statistic should he report? Round to the nearest hundredth.

The janitor calculates a p-value for the hypothesis test of approximately 0.113. Choose the correctinterpretation for the p-value.

A researcher conducts a hypothesis test on a population proportion. Her null and alternativehypothesis areH0: p=0.6 andHa: p<0.6. The test statistic and p-value for the test are z=-1.51andp-value=0.0655.For a significance level of?=0.05, choose the correct conclusion regardingthe null hypothesis.

From the TI-84 graphing calculator screenshots below, choose the screenshot whose shaded area depicts a p-value for a two-tailed test.

Suppose that the following is to be tested: $\mathrm { H } _ { 0 } : \mathrm { p } = 0.35$ and $\mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.35$ . Calculate the observed $z$ -statistic for the following sample data: Forty out of eighty test subjects have the characteristic of interest. Round to the nearest hundredth.

A researcher believes that children who attend elementary school in a rural setting are more physically active 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 reported participating in at least one hour of rigorous activity a day. The data is summarized in the table below. Assume the all conditions for proceeding with a two-sample test have been met. Rural Urban =90 =78 =74 =55 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, $\mathrm { H } _ { 0 }$ : prural = purban.

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

List and briefly summarize the essential ingredients of the hypothesis test.