Question

Calculate the p value

11.4.4-T Question Help Jse the following information to complete steps (a) through (d) below. A random sample of n, - 110 individuals results in x, = 40 successes. An independent sample of nz - 140 individuals results in X2 = 60 successes. Does this represent sufficient evidence to conclude that p, <P2 at the q=0.05 level of significance? ระทานและจรดมานผล 0.ruguarษานา นาurer useur 4๒๕๖uatu Vaาณ ด ต าแนะนมกณมน มานน (6) Determine the null and alternative hypotheses. Choose the correct answer below, MA. Ho: PP2i Hy: P<P2 8. Ho: P, > Pz: H :P, <P2 OG Ho: P.-P2iHqi Pz * P2 Ho: P1 - P2: H: P1 P2 (c) Use technology to calculate the P-value. (Round to three decimal places as needed.)

Answer 1

we know that null hypothesis always contain equality in it .

so in case of (b) option (A) is correct.

For sample 1, we have that the sample size is Ni = 110, the number of favorable cases is X1 = 40, so then the sample proportion is f1 = = 10 = 0.3636 For sample 2, we have that the sample size is N2 = 140, the number of favorable cases is X2 = 60, so then the sample proportion is p2 = = 1600 = 0.4286 The value of the pooled proportion is computed as p = 10---60 110-140 = 0.4 Also, the given significance level is a = 0.05. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: P1 = P2 Ha: Pi<P2 This corresponds to a left-tailed test, for which a z-test for two population proportions needs to be conducted. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a left-tailed test is ze = -1.64. The rejection region for this left-tailed test is R={z: < -1.64} (3) Test Statistics The z-statistic is computed as follows: P1 - 2 VP(1-7)(1/nı +1/n2) 0.3636 -0.4286 0.4.(1 -0.4)(1/110 + 1/140) = -1.04 (4) Decision about the null hypothesis Since it is observed that z = -1.04 > 2c = -1.64, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.1491, and since p = 0.1491 > 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion pı is less than P2, at the 0.05 significance level.

and p value is = 0.1491

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