Question

1. You want to do a study to determine the mean amount of time, in hours, an SMC student spends at a paid job each week. Initial studies indicate that there is a standard deviation of 4.6 hours. The result should be found to 95% confidence to within 0.5 hours. How many SMC students should you poll?

a. 18 students

b. 30 students

c. 19 students

d. 326 students

e. 325 students

2. The Graduate Management Admission Test (GMAT) is a test required for admission into many masters of business administration (MBA) programs. Total scores on the GMAT are normally distributed. The Graduate Management Admission Council, who administers the test, claims that the mean total score less than 579. (Source: http://www.mba.com/.) Suppose a random sample of 8 students took the test, and their scores are given below.

699, 560, 414, 570, 521, 663, 727, 413

Perform the appropriate hypothesis test to determine if the mean score is less than 579. Use a 0.05 level of significance.

e) Find the claim, the null hypothesis and the alternative hypothesis for this situation.

Claim:    [">", "<", "="]                                    [ Select ]                       ["529", "579", "571"]      

Ho:       [">", "<", "="]                                    [ Select ]                       ["529", "579", "571"]      

H₁:     [">", "=", "<"]                                    [ Select ]                       ["570", "529", "579"]      

f) Use the appropriate calculator function to find the p-value for this test. Round to four decimal places.

a. -0.1909

b. 0.1909

c. 0.8540

d. 0.4270

e. 0.5730

g) What comparison is used to reach a conclusion in this hypothesis test?

p-value                            [ Select ]                       [">", "=", "<"]                                    [ Select ]                       ["0.5", "0.01", "0.05", "0.10"]      

f) What conclusion is reached?

a. Do not reject Ho: There is not sufficient evidence to support the claim that the mean score is less than 579.

b. Do not reject Ho: There is sufficient evidence to support the claim that the mean score is less than 579.

c. Reject Ho: There is sufficient evidence to support the claim that the mean score is greater than 579.

d. Reject Ho: There is not sufficient evidence to support the claim that the mean score is less than 579.   

g) What is the possible error type in this problem?

a. Beta

b. Type 2

c. Type 1

d. Alpha

h) Interpret the p-value in a sentence.

Assuming that ("The Claim", "The p-value", "The alternative hypothesis, Ho", "The null hypothesis, Ho") is true, the probability of obtaining ("The level of significance", "The p-value", "The sample information", "The mean of 579") or values more extreme is ("-0.1909", "0.8540", "0.5730", "0.4270", "0.1909")

Answer 1