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Chapter 11: Q.20 (page 694)

The chi-square statistic is

(a) (18-25)225+(22-25)225+(39-25)225+(21-25)225

(b) (25-18)218+(25-22)222+(25-39)239+(25-21)221

(c) (18-25)25+(22-25)25+(39-25)25+(21-25)25

(d)(18-25)2100+(22-25)2100+(39-25)2100+(21-25)2100

(e)(0.18-0.25)20.25+(0.22-0.25)20.25+(0.39-0.25)20.25+(0.21-0.25)20.25

Short Answer

Expert verified

The correct answer is

(a)(18-25)225+(22-25)225+(39-25)225+(21-25)225

Step by step solution

01

Given information

Given in the question that, Researchers wondered whether the trees in a longleaf pine forest in Georgia are randomly distributed. To find out, they divided the forest into four equal quadrants. Then the researchers took a random sample of 4trees and counted the number in each quadrant. Here are their data:

02

Explanation

QuadraticCount
1
18
2
22
3
39
4
21

The formula to compute the test statistic is

蠂2=鈭�(O-E)2/E

03

Step 3:Calculation for test statistic 

The calculation for test statistic could be done as:

Observed Value(O)Expected value(E)

18

0.25(100)=25

22

0.25(100)=25

39

0.25(100)=25
21
0.25(100)=25

The test statistic is:

蠂2=鈭�(O-E)2E

=(18-25)225+(22-25)225+(39-25)225+(21-25)225

Thus, the test statistic is (18-25)225+(22-25)225+(39-25)225+(21-25)225

Thus, the correct option is (a).

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Most popular questions from this chapter

Removing warts A recently reported study looked at the use of oral zinc supplements to get rid of warts. The treatment group took an oral zinc supplement. Of these 32people, 19were rid of their warts after one month, and 6additional patients were rid of them after two months. The 23subjects in a control group were given a placebo. Of these, 1was rid of his warts after one month and 2additional patients were rid of their warts after two months. The reported results of the study included this table.

(a) The researchers say they did a chi-square test on this table. Explain why that makes no sense. Then make a correct two-way table displaying the results of the experiment.

(b) Explain why it is not appropriate to use a chi-square test in this setting even with the correct two-way table.

Which of the following explains why one of the conditions for performing the chi-square test is met in this case?

(a) The sample is large, 4877teenagers in all.

(b) The sample is random.

(c) All the observed counts are greater than 100.

(d) We used software to do the calculations.

(e) Both variables are categorical.

Researchers looked at a random sample of 1509full-page ads that show a model in magazines aimed at young men, at young women, or at young adults in general. They classified the ads as 鈥渘ot sexual鈥� or 鈥渟exual,鈥� depending on how the model was dressed (or not dressed). Here are the data:

The figure below displays Minitab output for a chi-square test using these data

a) Which type of chi-square test should be used in this case? Justify your answer.

(b) State an appropriate pair of hypotheses for the test you chose in part (a).

(c) Show how each of the numbers 60.94,424.8,and 12.835was obtained for the 鈥渘otsexy, Women鈥� cell

(d) Assuming that the conditions for performing inference are met, what conclusion would you draw? Explain

Does eating chocolate trigger headaches? To find out, women with chronic headaches followed the same diet except for eating chocolate bars and carob bars that looked and tasted the same. Each subject ate both chocolate and carob bars in random order with at least three days between. Each woman then reported whether or not she had a headache within 12hours of eating the bar. Here is a two-way table of the results for the 64subjects:

The researchers carried out a chi-square test on this table to see if the two types of bar differ in triggering headaches. Explain why this test is incorrect.

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Explain carefully why it would not be appropriate to perform a chi-square goodness-of-铿乼 test using these data.
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