A sample of size 9 from a normal distribution with 2 = 25 is used to test H0: = 20 H1: = 28

A sample of size 9 from a normal distribution with σ2 = 25 is used to test H0: µ = 20 H1: µ = 28

The test statistic used is the sample mean,X bar. Let us agree to reject H0 in favor of H1 if the observed value of Xbar is greater than 25.

(a) If H(0) is true, what is the distribution of Xbar?

(b) In the diagram, shade the region whose area in alpha

(c) Find alpha. Remember that alpha is computed under the assumption that H(0) is true.

(d) If H(1) is true, what is the distribution of Xbar?

(e) In the diagram, shade the region whose area is beta. Remember that beta is computed under the assumption that H(1) is true

(f) Find beta.

(g) Find the power of the test The test statistic used is the sample mean, . Let us agree to rejectH0 in favor of H1 if the observed value of is greater that 25.

(h) If the sample size is increased, the standard deviation of Xbar will decrease. What is thegeometric effect of this on the two curves in the Fig. 1?

(i) If the sample size is increased but the critical point is not changed, what will be the effect on alpha and beta?

 

y 20 25 28