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Chapter 11: Q. 11 (page 735)

A large distributor of gasoline claims that 60%all cars stopping at their service stations choose regular unleaded gas and that premium and supreme are each selected 20%of the time. To investigate this claim, researchers collected data from a random sample of drivers who put gas in their vehicles at the distributor's service stations in a large city. The results were as follows:

Carry out a significance test of the distributor's claim. Use a 5%significance level.

Short Answer

Expert verified

There is sufficient evidence to reject the distributor's claim.

Step by step solution

01

Given Information

Need to find whether there is sufficient evidence to reject the distributor's claim.

02

Explanation

Determine the observed frequencies and the chi-square subtotals:

The value of the test statistic is thus:

蠂2=1.8675+10.5125+0.8=13.15

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table C containing the t-value in the row

df=c-1=3-1=2

0.001<P<0.0025

If the P-value is less than or equal to the significance level, then the null hypothesis is rejected:

localid="1650541589569" P<0.05=5%鈬�RejectH0

There is sufficient evidence to reject the distributor's claim.

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Most popular questions from this chapter

Roulette Casinos are required to verify that their games operate as advertised. American roulette wheels have 38slots18red, 18black, and 2green In one casino, managers record data from a random sample of spins of one of their American roulette wheels. The one-way table below displays the results.

(a) State appropriate hypotheses for testing whether these data give convincing evidence that the distribution of outcomes on this wheel is not what it should be.

(b) Calculate the expected counts for each color. Show your work.

Refer to Exercise 27. Do the data provide convincing evidence of a difference in the distributions of sports goals for male and female undergraduates at the university?

(a) State appropriate null and alternative hypotheses for a significance test to help answer this question.

(b) Calculate the expected counts. Show your work.

(c) Calculate the chi-square statistic. Show your work

From exercise27

Canada has universal health care. The United States does not but often offers more elaborate treatment to patients with access. How do the two systems compare in treating heart attacks? Researchers compared random samples of 2600U.S. and 400Canadian heart attack patients. One key outcome was the patients鈥� own assessment of their quality of life relative to what it had been before the heart attack. Here are the data for the patients who survived a year:

Quality of lifeCanadaUnited StatesMuch better75541Somewhat better71498About the same96779Somewhat worse50282Much worse1965Total3112165

Is there a significant difference between the two distributions of quality-of-life ratings? Carry out an appropriate test at the 伪=0.01level.

Mars, Inc., reports that their M&M鈥橲 Peanut Chocolate Candies are produced according to the following color distribution: 23% each of blue and orange, 15% each of green and yellow, and 12% each of red and brown. Joey bought a bag of Peanut Chocolate Candies and counted the colors of the candies in his sample: 12 blue, 7 orange, 13 green, 4 yellow, 8 red, and 2 brown.

Calculate the expected count for each color, assuming that the company鈥檚 claim is true. Show your work.

Refer to Exercises 1 and 3.

(a) Confirm that the expected counts are large enough to use a chi-square distribution. Which distribution (specify the degrees of freedom) should you use?

(b) Sketch a graph like Figure 11.4 (page 683) that shows the P-value.

(c) Use Table C to find the P-value. Then use your calculator鈥檚 C2cdf command

(d) What conclusion would you draw about the company鈥檚 claimed distribution for its deluxe mixed nuts? Justify your answer.
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