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Chapter 11: Q. 43 (page 755)

Finger length Is your index finger longer than your ring finger? Or is it the other way around? It isn't the same for everyone. To investigate if there is a relationship between gender and relative finger length, we selected a random sample of 460U.S. high school students who completed a survey. The two-way table shows the results.


Do these data provide convincing evidence at the 伪=0.10level of an association between gender and relative finger length in the population of students who completed the survey?

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 gender and relative finger length.

H伪is there is an association between gender and relative finger length.

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

More candy The two-way table shows the results of the experiment

described in Exercise 27.


Red SurveyBlue Survey
Control Survey
Total
Red Candy13
5
8
26
Blue Candy
7
15
12
34
Total20
20
20
60

a. State the appropriate null and alternative hypotheses.

b. Show the calculation for the expected count in the Red/Red cell. Then provide a

complete table of expected counts.

c. Calculate the value of the chi-square test statistic.

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.

Is your random number generator working? Use your calculator鈥檚 RandInt function to generate 200 digits from 0 to 9 and store them in a list.

a. State appropriate hypotheses for a chi-square test for goodness of fit to determine whether your calculator鈥檚 random number generator gives each digit an equal chance of being generated.

b. Carry out a test at the 伪=0.05 significance level. Hint: To obtain the observed

counts, make a histogram of the list containing the 200 random digits, and use the trace feature to see how many of each digit were generated. You may have to adjust your window to go from 鈭�0.5to9.5 with an increment of 1

c. Assuming that a student鈥檚 calculator is working properly, what is the probability that the student will make a Type I error in part (b)?

d. Suppose that 25 students in an AP庐 Statistics class independently do this exercise for homework and that all of their calculators are working properly. Find the probability that at least one of them makes a Type I error.

All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer. The lower frequencies associated with household current are generally assumed to be harmless. To investigate the relationship between current configuration and type of cancer, researchers visited the addresses of a random sample of children who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either a high-current configuration (HCC) or a low-current configuration (LCC). Here are the data:

Computer software was used to analyze the data. The output included the value X2=0.435

Which of the following is the appropriate degrees of freedom for the X2test?

a. 1

b. 2

c. 3

d. 4

e. 5

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, 鈥淭wo-sample z test for the difference between two proportions.鈥� 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.
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