Question

A study of 45 pregnant women with more than 12 years of education were asked to predict the sex of their babies, and 32 of them made correct predictions. Use these results to test the claim that women with more than 12 years of education have a proportion of correct predictions that is greater than the 0.5 proportion expected with random guesses. Use a 0.01 significance level. Do these women appear to have an ability to correctly predict the sex of their babies? Must show all work.

Answer 1

The following information is provided: The sample size is N=45, the number of favorable cases is X=32, and the sample proportion is

, and the significance level is α=0.01

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:p=0.5

Ha: p>0.5

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 α=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:

(4) Decision about the null hypothesis

Since it is observed that z=2.832>zc​=2.33, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0023, and since p=0.0023<0.01, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is greater than p0​, at the α=0.01 significance level. Yes these women do appear to have an ability to correctly predict the sex of their babies.

Graphically

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