Question

You are interested in the gender proportions in different countries. You take a random sample of 41 Canadians and find that 21 of them are female. You take a random sample of Chinese citizens and find that of 60 people, 25 are female. Is this good evidence that there are a higher proportion of females in Canada than in China? Use α = 0.05 . What is the value of the p-value (to four decimal places)?

Answer 1

The p-value of 0.0417 suggests that there is sufficient evidence at a 5% significance level to conclude that there is a difference in the proportions of females between Canada and China. Since the p-value is less than the alpha level of 0.05, we reject the null hypothesis.

Step-by-step explanation:

In considering whether there is a higher proportion of females in Canada than in China based on a random sample, a hypothesis test for two proportions is used. The null hypothesis (H0) would state that the proportions of females in both countries are equal, while the alternative hypothesis (Ha) suggests that the proportions are different.

To calculate the p-value, one can use a statistical test such as the 2-PropZTest. You mentioned a p-value of 0.0417, which is the probability of observing a sample as extreme as the one collected, given that the null hypothesis is true.

Comparing the p-value to the significance level (Alpha: 0.05), the p-value is smaller (0.0417 < 0.05). Therefore, you would reject the null hypothesis, concluding that there is sufficient evidence at the 5 percent level to suggest a difference in the proportions of females between Canada and China.