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Chapter 11: Q.1.3 (page 681)

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 chi-square statistic for Joey’s sample. Show your work.

Short Answer

Expert verified

The test statistic is 11.3724

Step by step solution

01

Given Information

Given that the number of blue, orange, green, yellow, red, and brown candies are 12,7,13,4,8and 2 respectively.

The proportions are23%,15%and 12%respectively.

02

Calculation for Test statistic

The formula to calculate the test statistic is

χ2=∑(O-E)2E

The test statistic is:

χ2=∑(O-E)2E

=11.372

Thus, the test statistic is 11.3724.

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Most popular questions from this chapter

Benford’s lawFaked numbers in tax returns, invoices, or expense account claims often display patterns that aren’t present in legitimate records. Some patterns are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford’s law.3 Call the first digit of a randomly chosen record X for short. Benford’s law gives this probability model for X (note that a first digit can’t be 0):

A forensic accountant who is familiar with Benford’s law inspects a random sample of invoices from a company that is accused of committing fraud. The table below displays the sample data.

(a) Are these data inconsistent with Benford’s law? Carry out an appropriate test at the α=0.05level to support your answer. If you find a significant result, perform follow-up analysis.

(b) Describe a Type I error and a Type II error in this setting, and give a possible consequence of each. Which do you think is more serious?

Gregor Mendel (1822–1884), 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’s prediction. What do you conclude?

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.

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

(a) H0:μ=25, where μ=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.

Aw, nuts! A company claims that each batch of its deluxe mixed nuts contains 52%cashews, 27%almonds,13%macadamia nuts, and 8% brazil nuts. To test this claim, a quality control inspector takes a random sample of 150nuts from the latest batch. The one-way table below displays the sample data.

(a) State appropriate hypotheses for performing a test of the company’s claim.

b) Calculate the expected counts for each type of nut. Show your work.
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