Question

> Use the following information to complete steps (a) through (d) below. A random sample of n = 110 individuals results in xy = 40 successes. An independent sample of n2 = 160 individuals results in X2 = 60 successes. Does this represeot sufficient evidence to conclude that p, <P2 at the a= 0.01 level of significance? (a) What type of test should be used? O A. A hypothesis best regarding the difference between two population proportions from dependent samples. OB. A hypothesis tost regarding two population standard deviations. OC. A hypothesis best regarding the difference of two means using a matched-pairs design OD. A hypothesis test regarding the difference between two population proportions from independent samples. ypothesis (6) Determine the null and altermative hypotheses. Choose the correct answer below O A Ho: Papa:My P<P2 OB. Ho: P = P2: Hy: P4<P2 CHO:D, P2: H: PHP2 OD. Ho: PD:H: P2 (c) Use technology to calculate the P-value. (Round to three decimal ploons as needed.) nts to conclud Ubrary (d) Draw a conclusion based on the hypothesis test. Choose the correct answer below ptions Click to select your arwert)

Answer 1

a) ans-> D)

b) - d)

d) ans-> C)

Hypotheses : To test null hypothesis H. : P1 – P2 = 0 against alternative hypothesis H1 :P1 - P2 < 0 Let @ 1, Ô 2 denote the respective sample proportions and n1, n2 denotes the sample sizes respectively. Here. 40 60 P1 0.364, n = 110, P2 = 0.375, n2 = 160 110 160 The test statistic can be written as: (Ậ1 - P2) P1*(1-P) ni + P2*(1-P2) n2 which under H, follows a standard normal distribution. Decision rule / Rejection region : We reject H, at 0.01 level of significance if P-value < 0.01 or if Zobs <-20.01 = -2.326348 0.4- 0.3 0.2 0.1 0.0 - Z Now, The value of the test statistic Zobs -0.190227 -0.190 (0.364 – 0.375) 0.3636*(1-0.3636) 0.3750*(1-0.3750) + 110 160 The critical value critical = -2.326348 -2.326 P-value = P(Z < Zobs) = P(Z < -0.190227) = 0.424565 0.4246 Conclusion : Since p-value > 0.01 and zobs * Zcritical = -2.326348, so We fail to reject Ho at 0.01 level of significance Hence, we can conclude that the the first population proportion is not significantly lesser than second population proportion.