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Chapter 11: Q. R 11.2 (page 763)

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.

Short Answer

Expert verified

The result is not valid because the five counts are less than the six expected ones.

Step by step solution

01

Given information

We need to find the reason for non validity of result.

02

Explanation

We know that

Expected counts are a product of row and column total divided by table total.

The anticipated counts must all be at least five for the chi-square test to work. The table shows that six predicted counts are less than five, indicating that the chi-square test conditions have not been met. As a result, the outcomes aren't reliable.

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Most popular questions from this chapter

More P-values For each of the following, find the P-value using Table C. Then calculate a more precise value using technology.

a. χ2=4.49,df=5

b. χ2=4.49,df=1

Do students who read more books for pleasure tend to earn higher grades in English? The boxplots show data from a simple random sample of 79 students at a large high school. Students were classified as light readers if they read fewer than 3 books for pleasure per year. Otherwise, they were classified as heavy readers. Each student’s average English grade for the previous two

marking periods was converted to a GPA scale, where A=4.0, A−=3.7, B+=3.3

Reading and grades (3.2) The scatterplot shows the number of books read and the English grade for all 79 students in the study. The least-squares regression line y^=3.42+0.024x has been added to the graph.

a. Interpret the slope and y intercept.

b. The student who reported reading 17 books for pleasure had an English GPA of 2.85. Calculate and interpret this student’s residual.

c. For this linear model, r2=0.083 Interpret this value.

A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race or ethnicity of the driver. The results are summarized in the following table.

The proportion of this city's population in each of the racial/ethnic categories listed is as follows.

We wish to test H0: The racial/ethnic distribution of traffic tickets in the city is the same as the racial/ethnic distribution of the city's population.

We compute the value of the χ2test statistic to be 6.57. Assuming that the conditions for inference are met, which of the following is the correct P-value?

a. Greater than0.20

b. Between 0.10and0.20

c. Between 0.05and0.10

d. Between 0.01and0.05

e. Less than0.01

Tuition bills A random sample of U.S. adults was recently asked, “Would you support or oppose major new spending by the federal government that would help undergraduates pay tuition at public colleges without needing loans?” The two-way table shows the responses, grouped by age.

Do these data provide convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults?

Recent revenue shortfalls in a midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25%tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of 50freshmen, 50sophomores, 50juniors, and 50seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. Here are the results:

Which null hypothesis would be appropriate for performing a chi-square test?

a. The closer students get to graduation, the less likely they are to be opposed to tuition increases.

b. The mean number of students who are strongly opposed is the same for each of the 4years.

c. The distribution of student opinion about the proposed tuition increase is the same for each of the 4years at this university.

d. Year in school and student opinion about the tuition increase are independent in the sample.

e. There is an association between year in school and opinion about the tuition increase at this university.
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