Question

In a survey of 180 females who recently completed high school, 75% were enrolled in college. In a survey of 160 males who recently completed high school, 65% were enrolled in college. At a = 0.06, can you reject the claim that there is no difference in the proportion of college enrollees between the two groups? Assume the random samples are independent. Complete parts (a) through (@). (a) Identify the claim and state Ho and H. The claim is "the proportion of female college enrollees is different than the proportion of male college enrollees." Let p, represent the population proportion for female college enrollees and P2 represent the population proportion for male college enrollees. State Ho and Ha Choose the correct answer below. O A. Ho: P1 P2 Ha: P4 SP2 OD. Ho: P1 SP2 OB. Ho: P1 P2 HP12P2 O E. Ho: P2 P2 C. Ho: P1 P2 Ha: P1 * P2 OF. Ho: P17 P2 Click to select your answer(s).

Answer 1

a) same as

Let P1 denotes the true proportion of first population and P2 denotes the true proportion of second population Hypotheses : To test null hypothesis H. : P1 = P2 against alternative hypothesis H1 :p1 + P2 Let P1, 2 denote the respective sample proportions and 11, 12 denotes the sample sizes respectively. Here, pi = 0.75, N1 = 180, p2 = 0.65, n2 = 160 The test statistic can be written as: (Pi-P2) Pi*(1-P) P2*(1-P2) + ni 12 which under H, follows a standard normal distribution. Decision rule / Rejection region : We reject H, at 0.06 level of significance if P-value < 0.06 or if |zobs | > 20.030 =1.880794 0.4 0.3 0.2 0.1 - 0.0 - N Now, The value of the test statistic obs (0.750 - 0.650) 0.750*(1-0.750) 0.650*(1-0.650) 180 160 = 2.014745 2.015 The critical value = 1.880794 +1.88 = -1.88, 1.88 P-value = P(|=| > Zobs) = 2 * P(Z < 2.014745) = 2 *(1 - 0.978034) = 0.043931 0.0439 Conclusion: Since p-value < 0.06 and 21 > Zcritical = 1.880794, so we reject H, at 0.06 level of significance Hence, we can conclude that the two population proportions are significantly different.

d) ans-> iv)

e) ans->A)