Final answer:
To test the president's claim, we will conduct a hypothesis test using a random sample of 155 community college students. We will set up the null and alternative hypotheses, calculate the test statistic, determine the critical value and rejection region, calculate the p-value, and make a decision based on the p-value and the level of significance.
Step-by-step explanation:
To test the president's claim, we will conduct a hypothesis test.
- Step 1: Set up the null and alternative hypotheses. The null hypothesis, denoted as H0, is that the true proportion of female students is equal to 50%. The alternative hypothesis, denoted as Ha, is that the true proportion of female students is greater than 50%.
- Step 2: Calculate the test statistic. We will use the sample proportion of females in the random sample, which is 88/155 = 0.5677, denoted as p-hat.
- Step 3: Determine the critical value and the rejection region. Since we are testing for a proportion, we will use a z-test. At the 0.01 level of significance, the critical value is 2.326, corresponding to the upper 1% of the standard normal distribution. The rejection region is any test statistic greater than 2.326.
- Step 4: Calculate the p-value. The p-value is the probability of obtaining a test statistic as extreme as the one calculated under the null hypothesis. In this case, we want to find the probability of observing 88 or more female students out of 155.
- Step 5: Make a decision and draw a conclusion. If the p-value is less than the level of significance (0.01 in this case), we reject the null hypothesis. If the p-value is greater than the level of significance, we fail to reject the null hypothesis. In this case, if the p-value is less than 0.01, we would reject the president's claim that more than 50% of all community college students are female.