Exam 8: Hypothesis Testing for Population Proportions

A research firm carried out a hypothesis test on a population proportion using a right-tailedalternative hypothesis. Which of the following z-scores would be associated with a p-value of0.04? Round to the nearest hundredth.

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 believes that the reading habits of men and women are different. He takes a random sample from each population and records the response to the question, "Did you read at least one book last month?" The null hypothesis is $\mathrm { H } _ { 0 }$ : $\mathrm { p } _ { \text {women } } = \mathrm { p } _ { \text {men. } }$ . Choose the correct alternative hypothesis.

Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p $p = 0.07$ (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: $\mathrm { H } _ { 0 } : \mathrm { p } = 0.07 \text { and } \mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.07$ -Suppose that the janitor tests 300 randomly selected light bulbs and finds that 27 bulbs are defective. What value of the test statistic should he report? Round to the nearest hundredth.

For the following description, state whether a oneproportion z-test or a two-proportionz-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 theproportions that support the tax differ for these age groups.

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

Shade the approximate area that would represent the p-value for the alternative hypothesis and z- the p-value. Round to the nearest thousandth. - $\text { The alternative hypothesis is a right-tailed with a z-score } = 0.21$

Suppose a city official conducts a hypothesis test to test the claim that the majority of voterssupport a proposed tax to build sidewalks. Assume that all the conditions for proceeding with aone-sample test on proportions have been met. The calculated test statistic is approximately 1.40with an associated p-value of approximately 0.081. Choose the conclusion that provides the bestinterpretation for the p-value at a significance level of?=0.05

A researcher wishes to test the claim that the proportion of children with blue eyes in hisregion is different than one in six, the national rate of blue eyes in children. State andexplain the null and alternative hypothesis that should be used to test the claim.

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

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

To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "white 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 120 adults with "white collar" jobs of which 25 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 $N ( 0,1 )$ distribution as the sampling distribution are satisfied. Find the values of the sample proportion, $\mathrm { p }$ , the test statistic, and the p-value associated with the test statistic. Round all values to the nearest thousandth.

Write a statement describing the meaning of the level of significance in the context of the hypothesis test.

A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are $\mathrm { H } _ { 0 } : \mathrm { p } = 0.4$ and $\mathrm { H } _ { \mathrm { a } } : \mathrm { p } < 0.4$ . The test statistic and $\mathrm { p }$ -value for the test are $\mathrm { z } = - 3.01$ and $\mathrm { p }$ -value $= 0.0013$ . For a significance level of $\alpha = 0.05$ , choose the correct conclusion regarding the null hypothesis.

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

Shade the approximate area that would represent the p-value for the alternative hypothesis and z the p-value. Round to the nearest thousandth. - $\text { The alternative hypothesis is a two-tailed with a z-score } = - 1.88$

Check that the conditions hold so that the sampling distribution of the z-statistic willapproximately follow the standard normal distribution. Are the conditions satisfied? If not, choosethe condition that is not satisfied.

A sociologist believes that the proportion of single men who attend church on a regularbasis is less than the proportion of single women. She takes a random sample from eachpopulation and records the proportion from each that reported that they attended churchon a regular basis. The null hypothesis is $\mathrm { H } _ { 0 } : \mathrm { pmen } ^ { = } \mathrm { p } _ { \text {women } }$ . State the correct alternative hypothesis with a sentence and symbolically.

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.

Use the following information to answer the question. A health foods shop owner is wondering if his customer's dailyvitamin supplement habits are in the same proportion as the general population of adults. The shop owner heard in a newsreport that 60% of all adults reported that they took a daily vitamin. The shop owner believes that his customers have agreater proportion of adults who take a daily vitamin, so he decides to conduct a hypothesis test using the following null andalternative hypothesis: H0: p=0.6 and Ha: p>0.6. The shop owner collected data from 50 randomly selected customers. -To continue the study, the shop owner decides to collect data from 60 customers between the ages of 22 and 27 to see whether the proportion in this age group is different from the general population of adults. From this sample, 26 reported that they took a daily vitamin. The null hypothesis for this test is $\mathrm { H } _ { 0 } : \mathrm { p } = 0.6$ . and the alternative hypothesis is $: \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.6$ . Assume that the conditions that must be met in order for us to use the $N ( 0,1 )$ distribution as the sampling distribution are satisfied. Find the values of the sample proportion, $\hat { p }$ , the observed test statistic, and the p-value associated with this observed value. Round all values to the nearest thousandth.