A clinical trial was conducted using a new method designed to increase the proba

Question

A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl. As of this writing, 964 babies were born to parents using the new method, and 868 of them were girls. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl. Identify the null hypothesis, altemative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution. Which of the following is the hypothesis test to be conducted? Ho:p>0.5 H1 : p=0.5 Ho:p#0.5 H1 : p= 0.5 Hope 0.5 H1 : p=0.5 What is the test statistic? OA. O C. OE. O B. Ho: p= 0.5 H: p 0.5 O D. Ho: p#0.5 H1: p> 0.5 OF, Ho : p=0.5 H1 : p #0.5 (Round to two decimal places as needed.) What is the P-value? P-value = (Round to four decimal places as needed.) What is the conclusion about the null hypothesis? 0 A. Reject the null hypothesis because the P-value is less than or equal to the significance level, O B. Reject the null hypothes ° C. Fail to reject the null hypothesis because the P-value is greater than the significance level, . 0 D. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, . What is the final conclusion? is because the P-value is greater than the significance level, .

Explanation / Answer

Given :-

sample size is N=964, number of favorable cases is X=868, and the sample proportion is p¯= N/X = ( 964/868 )=0.9004, and the significance level is =0.01

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p = 0.05

Ha: p > 0.05

This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used.

(2) Rejection Region

Based on the information provided, the significance level is =0.01, and the critical value for a right-tailed test is zc=2.33.

The rejection region for this right-tailed test is R={z:z>2.33}

(3) Test Statistics

The z-statistic is computed as follows:

z=(p¯p0)/[ p0 ( 1- p0) /n ]

= (0.90040.05) / [ 0.05*(1-0.05)/964 ]=121.15

(4) Decision about the null hypothesis

Since it is observed that z=121.15 > zc=2.33, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0, and since p=0<0.01, it is concluded that the null hypothesis is rejected.

Option ( A) for conclusion.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p is greater than p0, at the =0.01 significance level.

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