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, 58 of the pregnant women had 12 years of education or less, and 36.2% 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. Choose the correct answer below. O A. Ho: p 0.362 O B. Ho: p 0.362 H1: p 0.362 O C. Ho: p 30.362 O D. Ho: pa 0.5 H1: p# 0.5 H1: 0.362 O E. Ho: p 30.5 O F Ho: p 0.5 H1: 0.5 H1: p

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.50

Alternative hypothesis: P 0.50

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.0657

z = (p - P) /

z = - 2.10

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -2.10 or greater than 2.10.

Thus, the P-value = 0.0358

Interpret results. Since the P-value (0.0358) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Do not reject H0. There is sufficient evidence to warant rejection of the claim that these women have no ability to predict sex of their baby. The results for these womens with 12 years of education or less suggests that their percentages of correct prediction is not very different from results expected with random guesses.

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