Exam 8: Hypothesis Testing for Population Proportions

A researcher believes that children who attend elementary school in a rural setting have lowerobesity rates then children who attend elementary school in an urban setting. The researchercollects a random sample from each population and records the proportion of children in eachsample who were clinically obese. The data is summarized in the table below. Assume the allconditions for proceeding with a two-sample test have been met. Rural Urban =95 =100 =14 =26 Find the z-statistic (rounded to the nearest hundredth) and p-value (rounded to the nearestthousandth) for this hypothesis test. Using a 5% significance level, state the correct conclusionregarding the null hypothesisH0:prural=purban.

A sociologist believes that families that eat at least one meal a day together (without theinterference of any other media) will have better communication skills. The sociologistconducts a study to see if there is a difference in the proportion of meals that are eatentogether as a family for families living in a rural setting compared to families living in anurban setting. She collects a random sample from each population and records theproportion of test subjects that reported that they had eaten at least 3 meals per weektogether as a family. The data is summarized in the table below. Assume the all conditionsfor proceeding with a two-sample test have been met. Rural Urban =75 =140 =12 =40 Find the z test statistic (rounded to the nearest hundredth) and p-value (rounded to the nearest thousandth) for testing the hypothesis that the population proportions are different. At the 5% significance level, state the correct conclusion regarding the null hypothesis $\mathrm { H } _ { 0 } : \text { prural } = \mathrm { p } _ { u r b a n }$ . Round all calculations to the nearest hundredth.

Suppose the store manager tests 150 pencils and finds that 9 are defective. Calculate the z test statistic. Round to the nearest hundredth.

Complete the statement by filling in the blanks. The null hypothesis is _{--------------------}to be_{--------------------} and is only rejected when the observed outcome is shown to be_{--------------------}

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

Which of the following is not one of the four steps of the hypothesis test?

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

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

Two different students conduct a coin flipping experiment with a left-tailed alternative.The obtain the following test statistics: Student $\# 1 : \mathrm { z } = - 2.05$ Student $\# 2 : \mathrm { z } = - 1.28$ Which of the test statistics has a smaller p-value and why?

From the TI-84 graphing calculator screenshots below, choose the screenshot whose shaded area correctly depicts the following hypothesis test results: $\mathrm { H } _ { 0 } : \mathrm { p } = 0.25 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } > 0.25 , \alpha = 0.05 , \mathrm { z } = 2.01 , \mathrm { p }$ -value $= 0.022$

Use the following information to answer the question. A child psychologist believes that controlled physical outbursts of anger (like punching a pillow) may improve the mood of young boys with emotional impairment. He believes that the proportion of boys that would benefit from this treatment is greater than the proportion of girls. A random sample from each population receives counseling in the treatment and is asked about their mood after an episode (x is the number of test subjects that reported an improvement in mood). The results of the study are summarized in the table below. Boys Girls =200 =210 =35 =28 -Find the percentage of children that reported an improved mood from each group.Compare the percentages. Do the initial (untested) findings show what the psychologist expected?

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.

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 andHa: p>0.6. The shop owner collected data from 50 randomly selected customers. -List and verify that the conditions hold so that the sampling distribution of the z test statistic will approximately follow the standard normal distribution.

Suppose the following is to be tested: $\mathrm { H } _ { 0 } : \mathrm { p } = 0.4$ and $\mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.4$ . Calculate the observed $\mathrm { z }$ test statistic for the following sample data: $n = 80$ and 25 test subjects have the characteristic of interest. 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 rate of asthma attacks in children ages 5 to 14 with asthma ages. The rate of asthma attacks in the population of concern is 0.0744.

Read the following then choose the appropriate test and name the population(s). A researcher asks random samples of men and women whether they had purchased organicallygrown food in the last three months. He wants to determine whether the proportion of women whopurchase organically grown food is greater than the proportion of men who purchase organicallygrown food.

Suppose that the following is to be tested: $\mathrm { H } _ { 0 } : \mathrm { p } = 0.72$ and $\mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.72$ . 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.

From the TI-84 graphing calculator screenshots below, choose the screenshot whose shaded area correctly depicts the following hypothesis test results: $\mathrm { H } _ { 0 } : \mathrm { p } = 0.15 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.15 , \alpha = 0.05 , \mathrm { z } = - 1.82 , \mathrm { p }$ -value $= 0.0688$

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

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