Question

Question 1 Based on information from Harper’s Index, 37 out of a random sample of 100 adult Americans who did not attend college believe in extra-terrestrials. However, from a random sample of 150 adult American who did attend college, 70 of them claim they believe in extra-terrestrials. a) State the null and alternate hypotheses to determine whether the proportion of people who did attend college and who believe in extra-terrestrials is higher than the proportions of those who did not attend college. b) What proportion of people who did not attend college believe in extra-terrestrials? What proportion of people who did attend college believe in extra-terrestrials? c) Calculate the test statistic. Show hand calculation. d) Using Minitab, test your hypothesis using a 5% significance level. e) Based on the p-value, interpret the results of this test. f) What are the assumptions in using the two-sample proportion test and have we met those conditions?

Answer 1

a) H₀: P1 = P2

    H₁: P1 < P2

b) = 37/100 = 0.37

   = 70/150 = 0.47

c) The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                                          = (0.37 * 100 + 0.47 * 150)/(100 + 150)

                                                          = 0.43

SE = sqrt(P(1 - P)(1/n1 + 1/n2))

      = sqrt(0.43 * (1 - 0.43) * (1/100 + 1/150))

      = 0.0639

The test statistic z = ()/SE

                             = (0.37 - 0.47)/0.0639 = -1.56

d) P-value = P(Z < -1.56)

                 = 0.0594

e) Since the P-value is greater than the significance level(0.0594 > 0.05), so we should not reject the null hypothesis.

So at 55 significance level there is not sufficient evidence to conclude that the proportion of people who did attend the college and who believe in extra-terrestrials is higher than the proportion of those who did not attend college.

f) The samples are simple random samples.

* n1 = 0.37 * 100 = 37

(1 - ) * n1 = (1 - 0.37) * 100 = 63

* n1 > 10 , (1 - ) * n1 > 10

* n2 = 0.47 * 150 = 70.5

(1 - ) * n2 = (1 - 0.47) * 150 = 79.5

* n2 > 10, (1 - ) * n2 > 10