1.The following null hypothesis is being tested:

Ho: < 150

Assume that the population standard deviation () is equal to 30.

a.What is the probability of making a Type I error when = 150, N = 50, and we have decided to reject Ho if we get a sample mean (x) > 155?

b. What is the probability of making a Type II error when u = 160, N = 100 and we have decided to accept Ho if the sample mean (x) is < 156?

c. In words, what do these probabilities mean?

2.A random sample 100 students is selected from a class.Their average monthly income is $510 with a standard deviation of $52.Using a significance level of .01, test the null hypothesis that > $525.

3.Test the following null hypotheses using a significance level of .05.

a. = 10; x = 10.1; s = .3; N = 100

b. > .72; x = .705; s = .13; N = 169

c. < 0; x = .7; s = 2.5; N = 626

d. = .5; p = .55; N = 100

4. A statistics professor takes a random sample of 25 students who have taken a special statistics class.He wants to test the null hypothesis that the grades of these students are, on average, less than or equal to those of the population of students who take the regular statistics test.The mean grade for the population is 75.The mean grade for the sample is 86 with a standard deviation of 10.Using a significance level of .05, test the null hypothesis.