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Chapter 11: Q.3 (page 692)

Aw, nuts! Calculate the chi-square statistic for the data in Exercise 1. Show your work.

Short Answer

Expert verified

From the given information, the test statistics are6.5988

Step by step solution

01

Given Information

It is given in the question that,

p1=52%=0.52

p2=27%=0.27

p3=13%=0.13

p4=8%=0.08

n=Samplesize=150

The one-way table below displays the sample data.

02

Step 2: Explanation

The null and alternative hypotheses are:

H0: p1=p2=p3

H伪: At least one of piis different.

The calculation for the test statistic is done as:

03

Explanation

The test statistics are:

蠂2=鈭�(O鈭�E)2/E=6.5988

Therefore, the test statistics are6.5988

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Most popular questions from this chapter

Refer to Exercise 28. Do the data provide convincing evidence of a difference in the distributions of opinions about how high schools are doing among black, Hispanic, and white parents?

(a) State appropriate null and alternative hypotheses for a significance test to help answer this question.

(b) Calculate the expected counts. Show your work.

(c) Calculate the chi-square statistic. Show your work.

Gregor Mendel (1822鈥�1884), an Austrian monk, is considered the father of genetics. Mendel studied the inheritance of various traits in pea plants. One such trait is whether the pea is smooth or wrinkled. Mendel predicted a ratio of 3smooth peas for every 1 wrinkled pea. In one experiment, he observed 423 smooth and133 wrinkled peas. The data were produced in such a way that the Random and Independent conditions are met. Carry out a chi-square goodness-of-fit test based on Mendel鈥檚 prediction. What do you conclude?

An appropriate null hypothesis to test whether the trees in the forest are randomly distributed is

(a) H0:渭=25, where 渭=the mean number of trees in each quadrant.

(b) H0:p=0.25, where p=the proportion of all trees in the forest that are in Quadrant 1.

(c) H0:n1=n2=n3=n4=25, where niis the number of trees from the sample in Quadrant i.

(d) H0:p1=p2=p3=p4=0.25, where piis the actual proportion of trees in the forest that are in Quadrant i.

(e) H0:p^1=p^2=p^3=p^4=0.25, where p^iis the proportion of trees in the sample that are in Quadranti.

Perform a follow-up analysis of the test in Exercise 40 by finding the individual components of the chi-square statistic. Which cell(s) contributed most to the final result?

No chi-square A school鈥檚 principal wants to know if students spend about the same amount of time on homework each night of the week. She asks a random sample of 50students to keep track of their homework time for a week. The following table displays the average amount of time (in minutes) students reported per night:

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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