Final answer:
To compare the pass rates, calculate the pooled proportion and the test statistic. Find the critical value for a right-tailed test at α = 0.05. The p-value is smaller than 0.05, so we reject the null hypothesis that the pass rates are the same.
Step-by-step explanation:
a. To compare the pass rates, we can calculate the pooled proportion by adding the number of successful graduates from both schools and dividing by the total number of graduates. For Fly-More Academy, the pass rate is 70/140 = 0.5, and for Blue Yonder Institute, the pass rate is 104/260 = 0.4. The pooled proportion is (70+104)/(140+260) = 0.433.
b. The test statistic for comparing two proportions is calculated using the formula: test statistic = (p₁ - p₂) / √(pooled proportion * (1 - pooled proportion) * ((1/n₁) + (1/n₂))). Using the values from the question, the test statistic is (0.5 - 0.4) / √(0.433 * (1 - 0.433) * ((1/140) + (1/260))) = 2.29.
c. The critical value for a right-tailed test at α = 0.05 can be found using a normal distribution table or a statistical software. For a significance level of 0.05, the critical value is approximately 1.645.
d. The p-value is the probability of obtaining a test statistic as extreme as the one calculated, assuming the null hypothesis is true. To find the p-value, we can use a statistical software or a t-distribution table. In this case, the p-value is smaller than 0.05, indicating strong evidence against the null hypothesis.
e. Based on the p-value being smaller than the significance level of 0.05, we reject the null hypothesis. This means that there is evidence to support the claim that the pass rates of the two aviation training schools are different.