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Chapter 11: Q 5. (page 716)

Aw, nuts! Refer to Exercise 1.

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’s χ2 cdf command.

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

Short Answer

Expert verified

Part (a) The df=3

Part (b) P-value =0.0858

Part (c) There isn't enough evidence to refute the claim concerning the probability distribution in question.

Step by step solution

01

Part (a) Step 1: Given information

Type of countCountFrequencyExpected
Cashew8352%78
Almond2927%40.5
Macadamia2013%19.5
Brazil188%12
Total150100%150

Chi square test statistic=6.60

02

Part (a) Step 2: Calculation

The projected counts are large enough to use a chi-square distribution if all predicted counts are at least 5This condition is satisfied.

The degrees of freedom =df=c-1=4-1=3

03

Part (b) Step 1: Given information

The degrees of freedom =df=3

04

Part (b) Step 2: Calculation

The p-value using table for df=3 is,

0.05<P<0.10

The excel formula, =CHIDIST(6.6,3)

P-value=0.0858

05

Part (c) Step 1: Calculation

Chi square test statistic=6.60

The degrees of freedom=df=c-1=4-1=3

P-value=0.0858

Here, p-value>0.05fail to reject H0

There isn't enough evidence to refute the claim concerning the probability distribution in question.

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Most popular questions from this chapter

P-values For each of the following, find the P-value using Table C Then

calculate a more precise value using technology.

a. χ2=19.03,df=11

b. χ2=19.03,df=3

Birds in the trees Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees are Douglas firs, 40% are ponderosa pines, and 6% are other types of trees. At a randomly selected time during the day, the researchers observed 156 red-breasted nuthatches: 70 were seen in Douglas firs, 79 in ponderosa pines, and 7 in other types of trees.

a. Do these data provide convincing evidence that nuthatches prefer particular types of trees when they’re searching for seeds and insects?

b. Relative to the proportion of each tree type in the forest, which type of trees do the nuthatches seem to prefer the most? The least?

Fruit flies Biologists wish to mate pairs of fruit flies having genetic makeup RrCc, indicating that each has one dominant gene (R) and one recessive gene (r) for eye color, along with one dominant (C) and one recessive (c) gene for wing type. Each offspring will receive one gene for each of the two traits from each parent, so the biologists predict that the following phenotypes should occur in a ratio of 9:3:3:1:

Assume that the conditions for inference are met. Carry out a test at the α=0.05 significance level of the proposed genetic model.

More candy The two-way table shows the results of the experiment

described in Exercise 27.


Red SurveyBlue Survey
Control Survey
Total
Red Candy13
5
8
26
Blue Candy
7
15
12
34
Total20
20
20
60

a. State the appropriate null and alternative hypotheses.

b. Show the calculation for the expected count in the Red/Red cell. Then provide a

complete table of expected counts.

c. Calculate the value of the chi-square test statistic.

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?

a. 1

b. 2

c. 3

d. 4

e. 5
See all solutions

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