Final answer:
To compare the pass rates of Math 1A and Math 1B, appropriate hypothesis testing can be conducted. The null hypothesis is that the pass rates are equal, and the alternative hypothesis is that they are different. By calculating the test statistic and p-value, the decision can be made about the null hypothesis at a given significance level. Type I error occurs when the null hypothesis is rejected when it is true, and Type II error occurs when the null hypothesis is not rejected when it is false.
Step-by-step explanation:
A. State an appropriate null hypothesis:
Null hypothesis (H0): The pass rates of Math 1A and Math 1B are equal.
B. State an appropriate alternative hypothesis:
Alternative hypothesis (Ha): The pass rates of Math 1A and Math 1B are different.
C. Define the random variable, P':
Random variable P' represents the proportion of students who pass the course.
D. Calculate the test statistic:
To calculate the test statistic, we can use the z-test formula: z = (P1 - P2) / sqrt(P'(1-P') * (1/n1 + 1/n2)), where P1 is the pass rate of Math 1A, P2 is the pass rate of Math 1B, and n1 and n2 are the sample sizes of Math 1A and Math 1B respectively.
E. Calculate the p-value:
To calculate the p-value, we compare the test statistic to the critical value from the standard normal distribution.
F. At the 5 percent level of decision, what is your decision about the null hypothesis?
If the p-value is less than 0.05, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
G. What is the Type I error?
Type I error is when we reject the null hypothesis when it is actually true, in this case, concluding that the pass rates of Math 1A and Math 1B are different when they are actually equal.
H. What is the Type II error?
Type II error is when we fail to reject the null hypothesis when it is actually false, in this case, failing to conclude that the pass rates of Math 1A and Math 1B are different when they are actually not equal.