Question

1. Consider the following hypothesis test:

H_o: μ ≤ 51

H₁:   μ > 51

      A sample of 60 is used and the population standard deviation is 8. Use α=0.05.

1. Z critical = _______________
2. Sample mean = 53.5, z calc = ______________. Do you reject Ho?
3. Sample mean = 51.8, z calc = ______________. Do you reject Ho?
4. The Pvalue for c is:_________________

Answer 1

Solution:

We are given the following hypothesis test:

H_o: μ ≤ 51

H₁:   μ > 51

Sample size = n = 60

Population standard deviation =

Level of significance = α = 0.05.

Part a) Z critical =..........?

Since H₁:   μ > 51 is > type, this is right tailed test.

Thus find an area = 1 - α = 1 - 0.05 = 0.95

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_critical = 1.645

Z critical = 1.645

Part b) Sample mean = 53.5, z calc = ____________?

.

Since > Z critical = 1.645, we reject H0.

Part c) Sample mean = 51.8, z calc = ______?

.

Since   < Z critical = 1.645, we do not reject H0.

Part d) The P-value for c is:......?

For right tailed test , P-value is:

P-value = P(Z > z test statistic)

P-value = P(Z > 0.77)

P-value =1 - P(Z < 0.77)

Look in z table for z = 0.7 and 0.07 and find corresponding area.

P( Z < 0.77 ) = 0.7794

thus

P-value =1 - P(Z < 0.77)

P-value =1 -0.7794

P-value =0.2206