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Chapter 11: Q. 47 (page 756)

Which test? Determine which chi-square test is appropriate in each of the following settings. Explain your reasoning.

a. With many babies being delivered by planned cesarean section, Mrs. McDonald’s statistics class hypothesized that there would be fewer younger people born on the weekend. To investigate, they selected a random sample of people born before1980 and a separate random sample of people born after1993. In addition to year of birth, they also recorded the day of the week on which each person was born.

b. Are younger people more likely to be vegan/vegetarian? To investigate, the Pew Research Center asked a random sample of 1480 U.S. adults for their age and whether or not they are vegan/vegetarian.

Short Answer

Expert verified

a) A chi-square test for homogeneity is used when we are interested in the distribution of two variables and there are several independent samples.

b) A chi-square test for independence is used when we are interested in the distribution of two variables and there is only one sample.

Step by step solution

01

Part (a) Step 1: Given information 

We have to tell about statistics class hypothesized that there would be fewer younger people born on the weekend. To investigate.

02

Part (a) Step 2: Explanation

A chi-square goodness-of-fit test will be used if we are only interested in the distribution of one variable.

A chi-square test for homogeneity is used when we are interested in the distribution of two variables and there are several independent samples.

A chi-square test for independence is used when we are interested in the distribution of two variables and there is only one sample.

Two variables are of interest: the year of birth and the day of the week. We should also notice that we have two independent samples, so the chi-square test for homogeneity should be used.

03

Part (b) Step 1: Given information 

We have to tell about are younger people more likely to be vegan/vegetarian.

04

Part (b) Step 2: Explanation

  • A chi-square goodness-of-fit test will be used if we are only interested in the distribution of one variable.
  • A chi-square test for homogeneity is used when we are interested in the distribution of two variables and there are several independent samples.
  • A chi-square test for independence is used when we are interested in the distribution of two variables and there is only one sample.
  • We're looking for two things: age and whether or not they're vegan or vegetarian. We should also keep in mind that we only have one random sample, thus we should apply the chi-square test to determine independence.

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Most popular questions from this chapter

A study conducted in Charlotte, North Carolina, tested the effectiveness of three police responses to spouse abuse: (1)advise and possibly separate the couple, (2)issue a citation to the offender, and (3)arrest the offender. Police officers were trained to recognize eligible cases. When presented with an eligible case, a police officer called the dispatcher, who would randomly assign one of the three available treatments to be administered. There were a total of 650cases in the study. Each case was classified according to whether the abuser was arrested within 6months of the original incident.

a. Explain the purpose of the random assignment in the design of this study.

b. State an appropriate pair of hypotheses for performing a chi-square test in this setting.

c. Assume that all the conditions for performing the test in part (b) are met. The test yields x2=5.063x2=5.063and aP-valueof0.0796. Interpret this P-value.

d. What conclusion should we draw from the study?

Skittles® 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: “The 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.”

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

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

c. How large a χ2test statistic would you need to have significant evidence against the company’s claim at the α=0.05 level? At the α=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.

Mendel and the peas 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 3 smooth peas for every 1 wrinkled pea. In one experiment, he observed 423 smooth and 133 wrinkled peas. Assume that the conditions for inference are met.

a. Carry out a chi-square test for goodness of fit for the genetic model that Mendel predicted.

b. In Chapter 9Exercise 49 you tested Mendel’s prediction using a one-sample z test for a proportion. The hypotheses were H0:p=0.75and Ha:p≠0.75where p= true proportion of smooth peas. Calculate the z statistic and P-value for this test. How do these values compare to the values from part (a)?

Seagulls by the seashore Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29% mud, and 15% rocks. The biologists chose 200 seagulls at random. Each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. In all, 128 seagulls landed on the sand, 61 landed in the mud, and 11 landed on the rocks.

a. Do these data provide convincing evidence that seagulls show a preference for where they land?

b. Relative to the proportion of each ground type on the shore, which type of ground do the seagulls seem to prefer the most? The least?

No chi-square The principal in Exercise 7 also asked the random sample of students to record whether they did all of the homework that was assigned on each of the five school days that week. Here are the data:
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