4 For the following situations develop the appropriate null

4 For the following situations, develop the appropriate null and alternative hypothesis and state what the consequences would be for Type I and Type II errors. a. The Standard Tire Company has introduced a new tire in Europe that will be guaranteed to last at least 30,000 kilometers. Standard Tire has hired an independent agency to determine if there is overwhelming evidence that their tires will last through the warranty period. b. Mrs. Russell, head product tester for Hathaway Tool Corporation, is testing a newly designed series of bar hooks. The hooks have been designed to give way if they get too hot. The previous design gave way at 240 degrees. Develop a test to determine if the newly designed hooks give way at a higher temperature than the previous design.

Solution

a)

Here,

Ho: u <= 30000 km
Ha: u > 30000 km

Thus, a type I error is incorrectly rejecting a true null hypothesis. Hence, in this case, it is saying that the mean life is greater than 30000 km, when in fact, it is not.

Also, a type II error is incorrectly failing to reject a false null hypothesis. In this case, it is saying that the mean life is not greater than 30000 km, when in fact, it is.

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b)

Here,

Ho: u <= 240 degrees
Ha: u > 240 degrees

Thus, a type I error is incorrectly rejecting a true null hypothesis. Hence, in this case, it is saying that the mean \"giving way\" temperature is greater than 240 degrees, when in fact, it is not.

Also, a type II error is incorrectly failing to reject a false null hypothesis. Hence, in this case, it is saying that the mean \"giving way\" temperature is not greater than 240 degrees, when in fact, it is.