Question

PLEASE ANSWER ALL QUESTIONS!

1. Irene is running an import/export business. A delivery service has promised a change in her delivery times. She decides to test them at the 5% level. Her current service averages delivery in 23 days with a 6 day standard deviation. She lets the new service deliver 30 packages, and the average delivery is 21 days.

Calculate the p-value.

Select one:

a. 1.83%

b. 93.28%

c. 3.36%

d. 6.72%

e. 46.64%

f. Almost 0%

2. Olive believes there has been a change in the number of mortgage defaults in the subprime industry. A trade article states that the average has been 29.3 defaults per thousand, with a standard deviation of 12.4. A survey of 68 firms reveals the average is currently 27.1. Olive wants to know if the change is significant at the 10% level.

Calculate the p-value.

Select one:

a. 42.79%

b. 1.46%

c. 7.21%

d. 85.58%

e. Almost 0%

f. 14.42%

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 23
Alternative Hypothesis, Ha: μ ≠ 23

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (21 - 23)/(6/sqrt(30))
z = -1.826

P-value Approach
P-value = 0.0672 = 6.72%

Option d)

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 29.3
Alternative Hypothesis, Ha: μ ≠ 29.3

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.64 and 1.64.
Hence reject H0 if z < -1.64 or z > 1.64

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (27.1 - 29.3)/(12.4/sqrt(68))
z = -1.463

P-value Approach
P-value = 0.1442 = 14.42%

Option f)