In a study of pregnant women and their ability to correctly predict the sex of t

Question

In a study of pregnant women and their ability to correctly predict the sex of their baby, 57 of the pregnant women had 12 years of education or less, and 40.4 % of them correctly predicted the sex of their baby. Use a 0.01 significance level to test the claim that these women have no ability to predict the sex of their baby, and the results are not significantly different from those that would be expected with random guesses.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

Identify the null and alternative hypotheses.

The test statistic is z equals_______. (Round to two decimal places as needed.)

The P-value is ______. (Round to four decimal places as needed.)

Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

Reject / Fail to reject H0. There is / is not sufficient evidence to warrant rejection of the claim that these women have no ability to predict the sex of their baby. The results for these women with 12 years of education or less suggests that their percentage of correct predictions is / is not very different from results expected with random guesses.

Explanation / Answer

Null and Alternative Hypothesis:

Null Hypothesis (H0): P = 0.5

Alternative Hypothesis (H1): p ¹0.5

z = (p^ - P ) / Ö ((PQ/n))

p^ = 0.404

n = 57

P = 0.5

z = (0.404-0.5)/Ö[(0.404*(1-0.404))/57)]

= -1.48

The test statistics is z = -1.48

P-value = 2 * P ( z < -1.48 )

               = 2 * 0.0694

               = 0.1388

The P-value is 0.1388

Here the p-value is greater than .01 (level of significance. We fail to reject the null hypothesis.

Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that these women have no ability to predict the sex of their baby. The result for these women with 12 years of education or less suggests that their percentage of correct predictions is not very different from result expected with random guesses .

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