Chapter 11: Q.4 (page 692)
Roulette Calculate the chi-square statistic for the data in Exercise . Show your work.
Short Answer
From the given information, the test statistics are
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Chapter 11: Q.4 (page 692)
Roulette Calculate the chi-square statistic for the data in Exercise . Show your work.
From the given information, the test statistics are
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Skittles Statistics teacher Jason Molesky 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, lime, 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 bag of Skittles with 60 candies.
(c) How large a C2 statistic would you need to get in order to have significant evidence against the company鈥檚 claim at the A 0.05 level? At the A 0.01 level?
(d) Create a set of observed counts for a bag with 60 candies that gives a P-value between 0.01 and 0.05. Show the calculation of your chi-square statistic.
Many popular businesses are franchises鈥攖hink of McDonald鈥檚. The owner of local franchise benefits from brand recognition, national advertising, and detailed guidelines provided by the franchise chain. In return, he or she pays fees to the franchise firm and agrees to follow its policies. The relationship between the local owner and the franchise firm is spelled out in a detailed contract.
One clause that the contract may or may not contain is the entrepreneur鈥檚 right to an exclusive territory. This means that the new outlet will be the only representative of the franchise in a specified territory and will not have to compete with other outlets of the same chain. How does the presence of an exclusive-territory clause in the contract relate to the survival of the business?
A study designed to address this question collected data from a random sample of new franchise firms. Two categorical variables were measured for each franchisor. First, the franchisor was classified as successful or not based on whether or not it was still offering franchises as of a certain date. Second, the contract each franchisor offered to franchisees was classified according to whether or not there was an exclusive-territory clause. Here are the count data, arranged in a two-way table:
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Do these data provide convincing evidence of an association between an exclusive territory clause and business survival? Carry out an appropriate test at the level.
Birds in the trees Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, % of the trees were Douglas 铿乺s, % were ponderosa pines, and % were other types of trees. At a randomly selected time during the day, the researchers observed red-breasted nuthatches: were seen in Douglas 铿乺s, in ponderosa pines, and in other types of trees. Do these data suggest that nuthatches prefer particular types of trees when they鈥檙e searching for seeds and insects? Carry out a chi-square goodness-of-铿乼 test to help answer this question.
Stress and heart attack You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The subjects 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 people 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 people in the exercise group and out 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.
Yahtzee In the game of Yahtzee, six-sided dice are rolled simultaneously. To get a Yahtzee, the player must get the same number on all dice.
(a) Luis says that the probability of getting a Yahtzee in one roll of the dice is . Explain why Luis is wrong.
(b) Nassir decides to keep rolling all 5 dice until he gets a Yahtzee. He is surprised when he still hasn鈥檛 gotten a Yahtzee afterrolls. Should he be? Calculate an appropriate probability to support your answer .
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