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Chapter 11: Q.2.3 (page 703)

Calculate the chi-square statistic. Show your work.

Short Answer

Expert verified

The chi-square statistic is 19.49.

Step by step solution

01

Given Information

The table is,

02

Explanation

The formula to compute the chi-square statistic is:

χ2=∑(Observed-Expected)2Expected

Calculation:

The expected counts are,

Use FacebookMain CampusCommon wealthSeveral times a month or less77.5653.44At least once a week220.25151.75At least once a day612.19421.81

The chi-sqaure statistic is calculated as:

χ2=∑(Observed - Expected2Expected

=(55-77.56)277.56+(76-53.44)253.44+(215-220.25)2220.25………+(394-421.81)2421.81

=19.49

Thus, the chi-square statistic is 19.49.

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Most popular questions from this chapter

Why men and women play sports Do men and women participate in sports for the same reasons? One goal for sports participants is social comparision—the desire to win or to do better than other people. Another is mastery—the desire to improve one’s skills or to try one’s best. A study on why students participate in sports collected data from independent random samples of 67 male and 67 female under-graduates at a large university 15 Each student was classified into one of four categories based on his or her responses to a questionnaire about sports goals. The four categories were high social comparison– high mastery (HSC-HM), high social comparison– low mastery (HSC-LM), low social comparison–high mastery (LSC-HM), and low social comparison–low mastery (LSC-LM). One purpose of the study was to compare the goals of male and female students. Here are the data displayed in a two-way table: Observed Counts for Sports Goals

(a) Check that the conditions for performing the chi-square test are met.

(b) Use Table C to find the P-value. Then use your calculator’s C2cdf command.

(c) Interpret the P-value from the calculator in context.

(d) What conclusion would you draw? Justify your answer.

Use FacebookMain CampusCommon wealthSeveral times a month or less5576At least once a week215157At least once a day640394Total Facebook users910627

Interpret the p-value from the calculator in context.

The P-value for a chi-square goodness-of-fit test is 0.0129. The correct conclusion is

(a) reject H0at α=0.05; there is strong evidence that the trees are randomly distributed.

(b) reject H0at α=0.05; there is not strong evidence that the trees are randomly distributed.

(c) reject H0at α=0.05; there is strong evidence that the trees are not randomly distributed.

(d) fail to reject H0at α=0.05; there is not strong evidence that the trees are randomly distributed.

(e) fail to reject H0at α=0.05; there is strong evidence that the trees are randomly distributed.

A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two-way table (omitting a few who refused to answer and one who claimed to be homeless):

a) Should we use a chi-square test for homogeneity or a chi-square test of association/independence in this setting? Justify your answer.

(b) State appropriate hypotheses for performing the type of test you chose in part (a). Minitab output from a chi-square test is shown below

(c) Check that the conditions for carrying out the test are met.

(d) Interpret the P-value in context. What conclusion would you draw?

Mars, Inc., reports that their M&M’S Peanut Chocolate Candies are produced according to the following color distribution: 23% each of blue and orange, 15% each of green and yellow, and 12% each of red and brown. Joey bought a bag of Peanut Chocolate Candies and counted the colors of the candies in his sample: 12 blue, 7 orange, 13 green, 4 yellow, 8 red, and 2 brown.

Calculate the expected count for each color, assuming that the company’s claim is true. Show your work.
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