9. Hypothesis Testing for One Sample

Which of the following is not a characteristic of the $t$ test?

Which of the following is not a conclusion of the central limit theorem?

The National Bureau of Economic Research (NBER) is a private, nonprofit, nonpartisan research organization. The NBER provides information for better understanding of how the U.S. economy works. Researchers at the NBER concentrate on four types of empirical research: developing new statistical measurements, estimating quantitative models of economic behavior, assessing the effects of public policies on the U.S. economy, and projecting the effects of alternative policy proposals.One of the NBER’s interests is the median income of people in different regions of the United States. The table at the right shows the annual incomes (in dollars) of a random sample of people (15 years and over) in a recent year in four U.S. regions: Northeast, Midwest, South, and West.

In Exercises 1–5, refer to the annual incomes of people in the table. Use for all tests.

Use technology to perform a sign test to test the claim that the median annual income in the Midwest is greater than \$30,000.

Which of the following is not a criterion for making a decision in a hypothesis test?

Which of the following is the correct sequence of steps in hypothesis testing for determining if two population means are similar?

Which of the following graphs best represents the rejection region for the hypothesis test with null hypothesis $H_0:p\le 8.1$?

Which of the following best describes the null hypothesis for an independent-samples t-test?

A popular theme park claims that their weekly attendance is around $100,000$. You believe that the weekly attendance is different than this claimed value, so you gather sample data. Write the null and alternative hypotheses.

A candy manufacturer seeking to minimize the variation in weights of their candies claims to produce candies with a standard deviation less than $0.300$ g. Write the null and alternative hypotheses.

A survey claimed that $30\%$ of adults prefer electric cars over traditional cars. A car manufacturer believes the true proportion is higher than $30\%$. To test this, they survey a random sample of $50$ adults and find that $19$ say they prefer electric cars. Determine which test statistic to use & calculate it.

Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

$H_0:$ $p=0.4$

$H_a:$ $p\ne 0.4$

In a certain hypothesis test, $H_0:p=0.4$, $H_a:p$ < $0.4$. You collect a sample and calculate a test statistic $z=-1.32$. Find the $P$-value.

Stem Cell Survey In a Newsweek poll of 882 adults, 481 (or 55%) said that they were in favor of using federal tax money to fund medical research using stem cells obtained from human embryos. A politician claims that people don’t really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Use the following probabilities related to determining whether the result of 481 is significantly high (assuming the true rate is 50%). Is 481 significantly high? What should be concluded about the politician’s claim? Explain.

P(respondent says to use the federal tax money) = 0.5

P(among 882, exactly 481 says to use federal tax money) = 0.000713

P(among 882,481 or more say to use federal tax money) = 0.00389

Final Conclusions

In Exercises 21–24, use a significance level of α = 0.05 and use the given information for the following:

State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: The mean pulse rate (in beats per minute) of adult males is 72 bpm. The hypothesis test results in a P-value of 0.0095.

Interpreting Power Chantix (varenicline) tablets are used as an aid to help people stop smoking. In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced abdominal pain (based on data from Pfizer, Inc.). If someone claims that more than 8% of Chantix users experience abdominal pain, that claim is supported with a hypothesis test conducted with a 0.05 significance level. Using 0.18 as an alternative value of p, the power of the test is 0.96. Interpret this value of the power of the test.