Question

1. It is desired to test the null hypothesis ? = 40 against the alternative hypothesis ? > 40 on the basis of a random sample from a population with standard deviation 4. (a) If the probability of a Type I error is to be 0.03 and the probability of Type II error is to be 0.08 for ? = 39, find the required size of the sample. (b) If a level .01 test is used, what is b(38), the probability of Type II error when ? = 38 ? 2. A trucking firm is suspicious of the claim that the average lifetime of certain tires is at least 28,000 miles. To check the claim, the firm puts 25 of these tires on its trucks and gets a mean lifetime of 27,573 miles with a standard deviation of 1358 miles. Carry out a test of hypothesis using a significance level 0.05.

          1. It is desired to test the null hypothesis ? = 40 against the
alternative hypothesis ? > 40 on the basis of a random sample
from a population with standard deviation 4.
(a) If the
probability of a Type I error is to be 0.03 and the probability of
Type II error is to be 0.08 for ? = 39, find the required size of
the sample. (b) If a level .01 test is used, what is b(38), the
probability of Type II error when ? = 38 ?
2. A trucking firm is suspicious of the claim that the average
lifetime of certain tires is at least 28,000 miles. To check the
claim, the firm puts 25 of these tires on its trucks and gets a
mean lifetime of 27,573 miles with a standard deviation of 1358
miles. Carry out a test of hypothesis using a significance level
0.05.

1. It is desired to test the null hypothesis ? = 40 against the
alternative hypothesis ? > 40 on the basis of a random sample
from a population with standard deviation 4.
(a) If the
probability of a Type I error is to be 0.03 and the probability of
Type II error is to be 0.08 for ? = 39, find the required size of
the sample. (b) If a level .01 test is used, what is b(38), the
probability of Type II error when ? = 38 ?
2. A trucking firm is suspicious of the claim that the average
lifetime of certain tires is at least 28,000 miles. To check the
claim, the firm puts 25 of these tires on its trucks and gets a
mean lifetime of 27,573 miles with a standard deviation of 1358
miles. Carry out a test of hypothesis using a significance level
0.05.

Added by Justin G.

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