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Chapter 11: Q. 34 (page 754)

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

contain only cashews, Brazil nuts, almonds, and peanuts. The Premium nuts are much

more expensive than the Deluxe nuts. A consumer group suspects that the two nut mixes

are really the same. To find out, the group took separate random samples of pounds of

each nut mix and recorded the weights of each type of nut in the sample. Here are the

data:

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

differ significantly.

Short Answer

Expert verified

We cannot perform a chi-square test, since the chi-square test requires the observational tallies rather than weights.

Step by step solution

01

Given information

We have been given the weights of different types of nuts in two mixes.

02

Explanation

We note that the given table contains weights, whereas we have not been given the observational checks for each cell. We will at that point not perform a chi-square test, because the chi-square test requires the observational checks rather than weights. That is, the variable is quantitative (numerical) rather than categorical and the chi-square test requires categorical factors.

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Most popular questions from this chapter

Skittles庐 Statistics teacher Jason Mole sky contacted Mars, Inc., to ask about the color distribution for Skittles candies. Here is an excerpt from the response he received: 鈥淭he original flavor blend for the Skittles Bite Size Candies is lemon, green apple, orange, strawberry and grape. They were chosen as a result of consumer preference tests we conducted. The flavor blend is 20 percent of each flavor.鈥�

a. State appropriate hypotheses for a significance test of the company鈥檚 claim.

b. Find the expected counts for a random sample of 60 candies.

c. How large a 蠂2test statistic would you need to have significant evidence against the company鈥檚 claim at the 伪=0.05 level? At the 伪=0.01 level?

d. Create a set of observed counts for a random sample of 60 candies that gives a P-value between 0.01 and 0.05 Show the calculation of your chi-square test statistic.

Sorry, no chi-square How do U.S. residents who travel overseas for leisure differ from

those who travel for business? The following is the breakdown by occupation.

Occupation
Leisure travelers (%)
Business travelers (%)
Professional/technical
36
39
Manager/executive
23
48
Retired
14
3
Student
7
3
Other
20
7
Total
100
100

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

significantly.

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?

Which of the following is the correct number of degrees of freedom for the chi-square test using these data?

a.4

b.8

c. 10

d.20

e.4876

No chi-square A school鈥檚 principal wants to know if students spend about the same amount of time on homework each night of the week. She asks a random sample of 50 students to keep track of their homework time for a week. The following table displays the average amount of time (in minutes) students reported per night.

Explain carefully why it would not be appropriate to perform a chi-square test for goodness of fit using these data.
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