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Chapter 11: 1 (page 692)

Aw, nuts! A company claims that each batch of its deluxe mixed nuts contains 52%cashews, 27%almonds,13%macadamia nuts, and 8% brazil nuts. To test this claim, a quality control inspector takes a random sample of 150nuts from the latest batch. The one-way table below displays the sample data.

(a) State appropriate hypotheses for performing a test of the company鈥檚 claim.

b) Calculate the expected counts for each type of nut. Show your work.

Short Answer

Expert verified

(a) The null hypothesis will be H0 : The observed count of each type of nuts in a group of 150nuts from latest batch are same as claimed count of nuts in a group of 150

Versus

H1: The observed counts of each type of nuts in a group of 150nuts from latest batch are not same as claimed count of nuts in a group of150.

(b)

Step by step solution

01

Part (a) Step 1: 

The hypotheses for performing a test of company's claim that each batch of its deluxe mixed nuts contains 52%cashews, $27 \%$ almonds, $13 \%$ macadamia and $8 \%$ brazil nuts whereas a random sample of 150 nuts from each batch is having the following composition.

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Most popular questions from this chapter

A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), 鈥淲here do you live now? That is, where do you stay most often?鈥� Here is the full two-way table (omitting a few who refused to answer and one who claimed to be homeless):

a) Should we use a chi-square test for homogeneity or a chi-square test of association/independence in this setting? Justify your answer.

(b) State appropriate hypotheses for performing the type of test you chose in part (a). Minitab output from a chi-square test is shown below

(c) Check that the conditions for carrying out the test are met.

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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 170new 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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Your teacher prepares a large container full of colored beads. She claims that 1/8of the beads are red, 1/4are blue, and the remainder are yellow. Your class will take a simple random sample of beads from the container to test the teacher鈥檚 claim. The smallest number of beads you can take so that the conditions for performing inference are met is

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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�

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