BackA nonprofit consumer organization says that less than 25% of the televisions the organization rated in a recent year have an overall score of 70 or more. In a random sample of 35 televisions the organization rated in a recent year, 23% have an overall score of 70 or more. At α=0.05, can you support the organization’s claim?
Taught Enough Math? In 1994, 52% of parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 256 of 800 parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did in 1994? Use the α = 0.05 level of significance?
"Political Pundits [See Problem 4 in Section 10.2A.] In his book, “The Signal and the Noise,” Nate Silver analyzed 733 predictions made by experts regarding political events. Of the 733 predictions, 338 were mostly true.
e. Determine the P-value based on the model from part (d).
f. Interpret the P-value."
You Explain It! ESPSuppose an acquaintance claims to have the ability to determine the birth month of randomly selected individuals. To test such a claim, you randomly select 80 individuals and ask the acquaintance to state the birth month of the individual. If the individual has the ability to determine birth month, then the proportion of correct birth months should exceed 1/12 ≈ 0.083, the rate one would expect from simply guessing.
b. Suppose the individual was able to guess nine correct birth months. The P-value for such results is 0.1726. Explain what this P-value means and write a conclusion for the test.
Testing Claims About Proportions
In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Births A random sample of 860 births in New York State included 426 boys. Use a 0.05 significance level to test the claim that 51.2% of newborn babies are boys. Do the results support the belief that 51.2% of newborn babies are boys?
In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim.
Claim: p ≠0.15, α=0.05. Sample statistics: p_hat = 0.12, n=500
[NW] Government Waste Gallup News Service conducted a survey of 1017 American adolts aged 18 years or older. The respondents were asked, “Of every tax dollar that goes to the federal government in Washington, D.C., do you believe 51 cents or more are wasted?” Of the 1017 individuals surveyed, 35% indicated that 51 cents or more is wasted. Gallup reported that 35% of all adolt Americans 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 4% and a 95% level of confidence.
What can be inferred from this survey?
"Infidelity According to menstuff.org, 22% of married men have “strayed” at least once during their married lives.
a. Describe how you might go about administering a survey to assess the accuracy of this statement."
"Spanking
In March 1995, The Harris Poll reported that 80% of parents spank their children. Suppose a recent poll of 1030 adult Americans with children finds that 781 indicated that they spank their children. If we assume parents’ attitude toward spanking has not changed since 1995, how many of 1030 parents surveyed would we expect to spank?
Do the results of the survey suggest that parents’ attitude toward spanking may have changed since 1995? Why?"
Testing Claims About Proportions
In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Medical Malpractice In a study of 1228 randomly selected medical malpractice lawsuits, it was found that 856 of them were dropped or dismissed (based on data from the Physicians Insurers Association of America). Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed. Should this be comforting to physicians?
Discarded Plastic Find the test statistic used for the hypothesis test described in Exercise 1.
Accept versus Do Not Reject In the United States, historically, 40% of registered voters are Republican. Suppose you obtain a simple random sample of 320 registered voters and find 142 registered Republicans.
a. Consider the hypotheses H₀: p = 0.4 versus H₁: p > 0.4. Explain what the researcher would be testing. Perform the test at the α = 0.05 level of significance. Write a conclusion for the test.
Testing Claims About Proportions
In Exercises 9–32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Online Friends A Pew Research Center poll of 1060 teens aged 13 to 17 showed that 57% of them have made new friends online. Use a 0.01 significance level to test the claim that half of all teens have made new friends online.
Job Search A Gallup poll of 195,600 employees showed that 51% of them were actively searching for new jobs. Use a 0.01 significance level to test the claim that the majority of employees are searching for new jobs
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: More than 35% of air travelers would choose another airline to have access to inflight Wi-Fi. The hypothesis test results in a P-value of 0.00001.