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Exam 8: Hypothesis Testing for Population Proportions

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Question 1

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

A) State the level of significance.
B) Check the conditions that are required for future computations.
C) Make a decision to either accept the null hypothesis or accept the alternative hypothesis.
D) State the null and alternative hypothesis about the population parameter.

E) None of the above
F) B) and C)

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Question 2

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

A)
B)

C)

D) None of the above
E) All of the above

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C

Question 3

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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: H₀: p = 0.025 and H_a: p > 0.025. -The store manager calculates a p- value for the hypothesis test of 0.0030. Write a statement explaining what the p- value means and how it should be interpreted.

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

Use the following information to answer the question. A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults who reported drinking once a week or less in the last month was 0.26. The researcher's null hypothesis for this test is H₀: p = 0.26 and the alternative hypothesis is H_a: p > 0.26. The researcher collected data from a random sample of 75 adults in the region of interest. -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 H0: p = 0.26 and the alternative hypothesis is Ha: 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 N(0, 1) distribution as the sampling distribution are satisfied. Find the values of the sample proportion, p^, the test statistic, and the p- value associated with the test statistic. Round all values to the nearest thousandth.

A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0: p = 0.4 and Ha: p < 0.4. The test statistic and p- value for the test are z = - 3.01 and p- value = 0.0013. For a significance level of a = 0.05, choose the correct conclusion regarding the null hypothesis.

For the following description, state whether a oneproportion 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.

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

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.

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: H₀: p = 0.6 and H_a: 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.

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: H₀: p = 0.6 and H_a: p > 0.6. The 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 to clearly state the decision regarding the null hypothesis.

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: H₀: p = 0.6 and H_a: 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 H0: p = 0.6. and the alternative hypothesis is :Ha: p × 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, p^, the observed test statistic, and the p- value associated with this observed value. Round all values to the nearest thousandth.

Use the following information to answer the question. A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults who reported drinking once a week or less in the last month was 0.26. The null hypothesis for this test is H₀: p = 0.26 and the alternative hypothesis is H_a: p < 0.26. The researcher collected data from 150 surveys he handed out at a busy park located in the region. -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.

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

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 = 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: H₀: p = 0.07 and H_a: p > 0.07. -The janitor calculates a p- value for the hypothesis test of approximately 0.087. Choose the correct interpretation for the p- value.

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. -Assuming the conditions for a two proportion z- test hold, state the alternative hypothesis then find the observed test statistic and p- value. State your decision regarding the null hypothesis, H0: p1 = p2. How do the test results compare to the expectations of the psychologist? Round to the nearest hundredth.

A sociologist believes that the proportion of single men who attend church on a regular basis is less than the proportion of single women. She takes a random sample from each population and records the proportion from each that reported that they attended church on a regular basis. The null hypothesis is H0: pmen = pwomen. State the correct alternative hypothesis with a sentence and symbolically.

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 = 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: H₀: p = 0.07 and H_a: p > 0.07. -Choose the statement that best describes the significance level in the context of the hypothesis test.

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: H₀: p = 0.025 and H_a: p > 0.025. -The alternative hypothesis is a right- tailed with a z- score = 0.21

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.