A sample of size 9 from a normal distribution with mu2 25 i

A sample of size 9 from a normal distribution with mu2 = 25 is used to test H0: mu = 20 H1: mu = 28

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

(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 X?

(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 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?

Fig. 1

plz help me for the whole problem. Thanks.

Solution

a)

the distribution will be the gauss shaped that have the highest point in 20

b)

using the gauss shaped with mean = 20 , only the part that is greater than 25 ( 25 or greater) that is alpha

c)

we need the standar deviation

d)

the distribution will be the gauss shaped with mean = 28

e)

the area that is below to 25 ( that is include the number 20 of the graph before)

for the other literals

I can gladly help you but you should post it in a new question