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Chapter 11: Q.1.2 (page 681)

Mars, Inc., reports that their M&M鈥橲 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鈥檚 claim is true. Show your work.

Short Answer

Expert verified

The expected values are 10.58,10.59,6.9,6.9,5.52and52 respectively

Step by step solution

01

Given Information

Given that

The number of blue, orange, green, yellow, red and brown candies are 12,7,13,4,8 and 2 respectively. The proportions are 23%,15% and 12% respectively.

02

Explanation

The expected values could be calculated by

Blue46(0.23)=10.58

Orange46(0.23)=10.59
Green46(0.15)=6.9
Yellow
46(0.15)=6.9
Red46(0.12)=5.52
Brown
46(0.12)=5.52

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Most popular questions from this chapter

Benford鈥檚 lawFaked numbers in tax returns, invoices, or expense account claims often display patterns that aren鈥檛 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 铿乺st digits of numbers in legitimate records often follow a model known as Benford鈥檚 law.3 Call the 铿乺st digit of a randomly chosen record X for short. Benford鈥檚 law gives this probability model for X (note that a 铿乺st digit can鈥檛 be 0):

A forensic accountant who is familiar with Benford鈥檚 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鈥檚 law? Carry out an appropriate test at the 伪=0.05level to support your answer. If you 铿乶d a signi铿乧ant 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?

Let鈥檚 continue our analysis of Joey鈥檚 sample of M&M鈥橲 Peanut Chocolate Candies from the previous Check Your Understanding (page 681). Here is the brief intro of the question:

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.

1. Confirm that the expected counts are large enough to use a chi-square distribution. Which distribution (specify the degrees of freedom) should we use?

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

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

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

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

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

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

Stress and heart attack You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say: One group took a four-month stress management program, another underwent a four-month exercise program, and the third received usual heart care from their personal physicians. In the next three years, only three of the 33people in the stress management group suffered 鈥渃ardiac events,鈥� defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, seven of the 34people in the exercise group and 12out of the 40 patients in usual care suffered such events.36

(a) Use the information in the news article to make a two-way table that describes the study results.

(b) What are the success rates of the three treatments in preventing cardiac events?

(c) Is there a significant difference in the success rates for the three treatments? Give appropriate statistical evidence to support your answer.

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鈥攖he desire to win or to do better than other people. Another is mastery鈥攖he desire to improve one鈥檚 skills or to try one鈥檚 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鈥� high mastery (HSC-HM), high social comparison鈥� low mastery (HSC-LM), low social comparison鈥揾igh mastery (LSC-HM), and low social comparison鈥搇ow 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鈥檚 C2cdf command.

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

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