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# Alternative Hypothesis

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12.17 M&M / Mars claims that at least 20% of the M&M's in each package are the new blue color. Set up the null and alternative hypotheses to test this claim.

12.21 An automobile company thinks that with new designs, its cars will last longer before having a problem. For this reason, the company wishes to extend the warranty that comes with the vehicle in hopes of attracting more customers. Before making this change, the idea is tested. Prior to the design changes, the cars lasted on the average 43 months before having a major problem. A sample consisting of 50 cars was tested. The cars lasted an average of 44 months before having a major problem. The standard deviation is 2 months.

(a) Set up the null and the alternative hypotheses to test if average time before having a major problem is longer than 43 months.

(b) Test your hypothesis using a = 0.05.

(c) Find the p value.

(d) Based on the p value, what can you conclude about the average time before having a major problem?

13.16 People who watch major league baseball may have noticed a decrease in the percentage of successful stolen bases. The increase in slide-step pitching motion and players who focus on homers may be behind the decline, according to an article in The New York Times, 24 May 1994. In 1993 there were 957 stolen bases in 1446 attempts, while in 1994 there were 807 stolen bases in 1193 attempts.

(a) Calculate the sample proportion of stolen bases for each year.

(b) Set up the hypotheses to test whether there has been a decrease in the percentage of successful stolen bases.

(c) At the 0.05 level of significance, has the percentage really decreased?

13.19 Selling personal computers is big business and consumers are becoming increasingly aware of vendor reputation. A recent study of two vendors of desktop personal computers reports on the units that need repair for DeIl Computer and Gateway 2000. Of 1584 computers manufactured by Dell Computer, 427 needed repair, while for Gateway 2000, 825 of 2662 computers needed repair.
(a) Calculate the sample proportion of computers needing repair for each company.

(b) Set up the hypotheses to test whether the proportion of computers needing repairs is different for the two companies.

(c) At the 0.05 level of significance, what can you conclude?

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#### Solution Summary

The solution addresses the following questions:

12.17 M&M / Mars claims that at least 20% of the M&M's in each package are the new blue color. Set up the null and alternative hypotheses to test this claim.

12.21 An automobile company thinks that with new designs, its cars will last longer before having a problem. For this reason, the company wishes to extend the warranty that comes with the vehicle in hopes of attracting more customers. Before making this change, the idea is tested. Prior to the design changes, the cars lasted on the average 43 months before having a major problem. A sample consisting of 50 cars was tested. The cars lasted an average of 44 months before having a major problem. The standard deviation is 2 months.

(a) Set up the null and the alternative hypotheses to test if average time before having a major problem is longer than 43 months.

(b) Test your hypothesis using a = 0.05.

(c) Find the p value.

(d) Based on the p value, what can you conclude about the average time before having a major problem?

13.16 People who watch major league baseball may have noticed a decrease in the percentage of successful stolen bases. The increase in slide-step pitching motion and players who focus on homers may be behind the decline, according to an article in The New York Times, 24 May 1994. In 1993 there were 957 stolen bases in 1446 attempts, while in 1994 there were 807 stolen bases in 1193 attempts.

(a) Calculate the sample proportion of stolen bases for each year.

(b) Set up the hypotheses to test whether there has been a decrease in the percentage of successful stolen bases.

(c) At the 0.05 level of significance, has the percentage really decreased?

13.19 Selling personal computers is big business and consumers are becoming increasingly aware of vendor reputation. A recent study of two vendors of desktop personal computers reports on the units that need repair for DeIl Computer and Gateway 2000. Of 1584 computers manufactured by Dell Computer, 427 needed repair, while for Gateway 2000, 825 of 2662 computers needed repair.
(a) Calculate the sample proportion of computers needing repair for each company.

(b) Set up the hypotheses to test whether the proportion of computers needing repairs is different for the two companies.

(c) At the 0.05 level of significance, what can you conclude?

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