An institute conducted a clinical trial of its methods for gender selection. The

Question

An institute conducted a clinical trial of its methods for gender selection. The results showed that 275 of 330 babies born to parents using a specific gender-selection method were boys. Use the sign test and a 0.05 significance level to test the claim that the method used is effective in increasing the of a boy. Since the test statistic falls within the critical region, reject the null hypothesis. There is sufficient evidence that the method used is effective in increasing the likelihood of a boy. Since the test statistic does not fall within the critical region, fail to reject the null hypothesis. There is insufficient evidence that the method used is effective in increasing the likelihood of a boy. Since the test statistic falls within the critical region, fail to reject the null hypothesis. There is sufficient evidence that the method used is effective in increasing the likelihood of a boy. Since the test statistic does not fall within the critical region, reject the null hypothesis. There is insufficient evidence that the method used is effective in increasing the likelihood of a boy.

Explanation / Answer

Answer to the question)

Theoretically P(boy) = 0.5

.It states that the method is effective for boy

Sample size (n) = 330

Number of boys (x ) = 275

Sample proportion p^ = x/ n

p^ = 275/330

p^ = 0.83

.

In order to test the hypothesis we need to find the test statistic

Z = (p^ - P) / sqrt(p*(1-p)/n)

.

on plugging the values we get

z = (0.83 - 0.50) / sqrt(0.5*0.5/330)

z = 11.9895

.

P value for such high Z value is always 0.000

.

Inference: Since the P value 0.000 < significance level 0.05 , we reject the null

.

Conclusion: Thus we conclude that the method is effective since the chances of boy are more than usual. The result is statistically significant.

.

Thus the correct answer choice is the first statement

Z critical value for 0.05 significance level is 1.645

We got Z statistic 11.9895 > Z critical 1.645 , this means the Z statistic falls in the critical region , and we reject the null hypothesis. There is sufficient evidence that the method is effective

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