A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study, 449 babies were born, and 250 of them were girls. Use the sample data with .01 significance level to test the claim that with this method, the probability of a baby being a girl is greater than 0.5.

a.) What is the hypothesis test to be conducted?
b.) What is the test statistic? Z=? (round to 2 decimal places)
c.) What is the P-value? (round to 4 decimal places)
d.) What is the conclusion?
e.) Does the method appear to be effective?

Which formulas do i need?

a. Ho: p = 0.5

Ha: p > 0.5

b) z = 2.41
c) p-value = 0.0080

d) reject the Ho; there is sufficient evidence to claim that the probability of a baby being a girl is greater than 0.5

To perform a hypothesis test for this scenario, you will need to use the one-sample proportion z-test. Here are the formulas you will need:

a.) Hypothesis test:
The null hypothesis (H0): The probability of having a girl is equal to 0.5.
The alternative hypothesis (H1): The probability of having a girl is greater than 0.5.

b.) Test statistic (Z-score):
Z = (p̂ - p0) / √((p0 * (1 - p0)) / n)
where p̂ is the sample proportion, p0 is the hypothesized proportion (0.5), and n is the sample size.

c.) P-value:
The P-value is determined using the standard normal distribution table or a statistical software. It represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

d.) Conclusion:
In the conclusion, you will compare the P-value to the significance level (0.01). If the P-value is less than 0.01, you reject the null hypothesis. Otherwise, if the P-value is greater than or equal to 0.01, you fail to reject the null hypothesis.

e.) Effective method:
Based on the conclusion of the hypothesis test, you can determine whether the method appears to be effective. If the null hypothesis is rejected, it suggests evidence in favor of the alternative hypothesis, implying that the method may be effective in increasing the probability of conceiving a girl. However, if the null hypothesis is not rejected, it implies that there is insufficient evidence to support the claim that the method is effective.

Now, let's proceed with answering the questions using the provided data.