Two professors at a local college developed new teaching curriculum designed to increase students' grades in math classes. In a typical developmental math course, 55% of the students complete the course with a letter grade of A, B, or C. In the experimental course, of the 19 students enrolled, 13 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the α = 0 level of significance? Complete parts (a) through (g).
(d) Determine the P-value using the binomial probability distribution. State your conclusion to the hypothesis test.
First, determine the P-value.
P-value:
(Round to three decimal places as needed)
Is there sufficient evidence to support the research that the experimental course is effective?
A: No, do not reject the null hypothesis because the P-value is greater than α. There is insufficient evidence to conclude that the experimental course is effective.
B: Yes, do not reject the null hypothesis because the P-value is greater than α. There is sufficient evidence to conclude that the experimental course is effective.
C: Yes, reject the null hypothesis because the P-value is less than α. There is sufficient evidence to conclude that the experimental course is effective.
D: No, reject the null hypothesis because the P-value is less than α. There is insufficient evidence to conclude that the experimental course is effective.
(e) Suppose the course is taught with 57 students and 39 complete the course with a letter grade of A, B, or C. Use this information to estimate the P-value.
Verify whether the normal model may now be used to approximate the P-value.
Because np0 = 10, the sample size is 5% of the population size, and the sample can be used to approximate the P-value using the normal model.
(Round to one decimal place as needed)