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Chapter 11: Q. 44 (page 755)

Regulating guns The National Gun Policy Survey asked a random sample of adults, "Do you think there should be a law that would ban possession of handguns except for the police and other authorized persons?" Here are the responses, broken down by the respondent's level of education:

Do these data provide convincing evidence at the α=0.05level of an association between education level and opinion about a handgun ban in the adult population?

Short Answer

Expert verified

No, the data is not convincing evidence at the level of an association.

Step by step solution

01

Given information

We need to find out whether the data provided is convincing evidence or not.

02

Explanation

We know that

The null hypothesis asserts that the variables are unrelated, whereas the alternative hypothesis asserts that they are.

H0is there is no association between opinion and education level.

Hαis there is an association between opinion and education level.

And expected frequencies are a product of row and column total divided by table total.

And The squared differences between the actual and predicted frequencies, divided by the expected frequency, make up the chi-square subtotals.

Therefore, the data is not convincing evidence at the level of an association.

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Most popular questions from this chapter

Sorry, no chi-square We would prefer to learn from teachers who know their subject. Perhaps even preschool children are affected by how knowledgeable they think teachers are. Assign 48three- and four-year-olds at random to be taught the name of a new toy by either an adult who claims to know about the toy or an adult who claims not to know about it. Then ask the children to pick out a picture of the new toy from a set of pictures of other toys and say its name. The response variable is the count of right answers in four tries. Here are the data:

The researchers report that children who were taught by the teacher claiming to be knowledgeable did significantly better (χ2=20.4,P<0.05), Explain why this result isn't valid.

Inference recap (8.1to 11.2) In each of the following settings, state which inference procedure from Chapter 8,9,10,or11you would use. Be specific. For example, you might answer, “Two-sample z test for the difference between two proportions.” You do not have to carry out any procedures.

a. What is the average voter turnout during an election? A random sample of 38cities was asked to report the percent of registered voters who voted in the most recent election.

b. Are blondes more likely to have a boyfriend than the rest of the single world? Independent random samples of 300 blondes and 300 nonblondes were asked whether they have a boyfriend.

Online banking A recent poll conducted by the Pew Research Center asked a random sample of 1846Internet users if they do any of their banking online. The table summarizes their responses by age. 23Is there convincing evidence of an association between age and use of online banking for Internet users?

Stress and heart attacks You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say:

One group took a four-month stress management program, another underwent a four-month exercise program, and the third received usual heart care from their personal physicians. In the next three years, only 3of the 33people in the stress management group suffered "cardiac events," defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, 7of the 34people in the exercise group and 12out of the 40patients in usual care suffered such events.

a. Use the information in the news article to make a two-way table that describes the study results.

b. Compare the success rates of the three treatments in preventing cardiac events.

c. Do the data provide convincing evidence at the α=0.05level that the true success rates for patients like these are not the same for the three treatments?

Testing a genetic model Biologists wish to cross pairs of tobacco plants having genetic makeup Gg, indicating that each plant has one dominant gene (G) and one recessive gene (g) for color. Each offspring plant will receive one gene for color from each parent. The Punnett square shows the possible combinations of genes received by the offspring.

The Punnett square suggests that the expected ratio of green (GG) to yellow-green (Gg) to albino (gg) tobacco plants should be 1:2:1. In other words, the biologists predict that 25%of the offspring will be green, 50%will be yellow-green, and 25%will be albino. To test their hypothesis about the distribution of offspring, the biologists mate 84randomly selected pairs of yellow-green parent plants. Of 84offspring, 23plants were green, 50were yellow-green, and 11 were albino. Do the data provide convincing evidence at the α=0.01 level that the true distribution of offspring is different from what the biologists predict?
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