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Chapter 11: Q 9. (page 718)

Munching Froot Loops Kellogg鈥檚 Froot Loops cereal comes in six colors:

orange, yellow, purple, red, blue, and green. Charise randomly selected 120 loops and noted the color of each. Here are her data:

Do these data provide convincing evidence at the 5% significance level that Kellogg鈥檚 Froot Loops do not contain an equal proportion of each color?

Short Answer

Expert verified

There is insufficient evidence to refute Kellogg's assertion that its Froot Loop includes an equal quantity of each flavor.

Step by step solution

01

Given information

Significance level: 5% = 0.05

02

Concept

Null hypothesis: H0

When the value of P is less than or equal to the significance level, the null hypothesis is rejected.

03

Explanation

The Pvalue is used to calculate the likelihood of a test statistic or a more extreme number.

The P-value in the appendix, which contains the X2value in the row df=5may be found in the chi-square distribution table.

0.15<P<0.20

When the value of Pis not less than or equal to the significance level, the null hypothesis is not rejected.

P>0.05: fail to reject H0

Hence, There is insufficient evidence to disprove the company's assertion that Kellogg's produces Froot Loop.

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Most popular questions from this chapter

All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of our homes. High-frequency EM radiation is thought to be a cause of cancer. The lower frequencies associated with household current are generally assumed to be harmless. To investigate the relationship between current configuration and type of cancer, researchers visited the addresses of a random sample of children who had died of some form of cancer (leukemia, lymphoma, or some other type) and classified the wiring configuration outside the dwelling as either a high-current configuration (HCC) or a low-current configuration (LCC). Here are the data:

Computer software was used to analyze the data. The output included the value X2=0.435

Which of the following is the appropriate degrees of freedom for the X2test?

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d. 4

e. 5

Aw, nuts! Refer to Exercise 1.

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b. Use Table C to find the P-value. Then use your calculator鈥檚 蠂2 cdf command.

c. What conclusion would you draw about the company鈥檚 claimed distribution for its deluxe mixed nuts?

Going nuts The UR Nuts Company sells Deluxe and Premium nut mixes, both of which

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Explain why we can鈥檛 use a chi-square test to determine whether these two distributions

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Roulette Refer to Exercise 2.

a. Confirm that the expected counts are large enough to use a chi-square distribution to calculate the P-value. What degrees of freedom should you use?

b. Use Table C to find the P-value. Then use your calculator鈥檚 蠂2 cdf command.

c. What conclusion would you draw about whether or not the roulette wheel is operating correctly?

The color of candy Inspired by the example about how background music influences

choice of entr茅e at a restaurant, a statistics student decided to investigate other ways to

influence a person鈥檚 behavior. Using 60volunteers, she randomly assigned 20volunteers

to get a 鈥渞ed鈥� survey, 20volunteers to get a 鈥渂lue鈥� survey, and 20volunteers to get a

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fifth questions were different. For example, the fourth question on the 鈥渞ed鈥� survey was

鈥淲hen you think of the color red, what do you think about?鈥� On the blue survey, the

question replaced red with blue. On the control survey, the last two questions were not

about color. As a reward, each volunteer was allowed to choose a chocolate candy in a red

wrapper or a chocolate candy in a blue wrapper. Here are segmented bar graphs showing

the results of the experiment. Describe what you see.
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