Question

Two professors at a local college developed a new teaching curriculum designed to increase students' grades in math classes. In a typical developmental math course, 48% of the students complete the course with a letter grade of A, B, or C. In the experimental course, of the 17 students enrolled, 11 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the a=0.1 level of significance? Complete parts (a) through (g). Because npo (1-0) = 4.2 '10, the normal model may not be used to approximate the P-value (Round to one decimal place as needed.) (c) Explain why this is a binomial experiment There is a fixed number of trials with two mutually exclusive outcomes The trials are independent and the probability of success is fixed at 0.48 for each trial. (Type an integer or a decimal. Do not found.) (d) Determine the P-value using the binomial probability distribution. State your conclusion to the hypothesis test Partial Credit First determine the P-value P-value = 0.128 (Round to three decimal places as needed.) Is there sufficient evidence to support the research that the experimental course is effective? O A Yes, reject the null hypothesis because the P-value is less than a There is sufficient evidence to conclude that the experimental course is effective B. Yes, do not reject the null hypothesis because the P-value is greater than a There is sufficient evidence to conclude that the experimental course is effective. XC. No, reject the null hypothesis because the P-value is less than a There is insufficient evidence to conclude that the experimental course is effective *. No, do not reject the null hypothesis because the P-value is greater than there is insufficient evidence to conclude that the experimental course is effective (e) Suppose the course is taught with 51 students and 33 complete the course with a letter grade of A, B or C Verify whether the normal model may now be used to estimate the P-value Because np. (1-P) - 10, the sample size is 5% of the population size and the sample the normal model be used to approximate the P-value (Round to one decimal place as needed.) Enter your answer in the answer box and then click Check Answer

Answer 1

Given :

e) X = 33, n = 51 and po = 0.48

npo(1-po) = 51 * 0.48 * (1 - 0.48) = 12.7

Because npo(1-po) = 12.7 > 10, the sample size is less than 5% of the population size ,and the sample follows the normal model which can be used to approximate the p value.

2) p₀ = 0.62, X = 242, n = 400

n * p₀ , n * (1 - p₀) = 400 * 0.62 * (1-0.62) = 94.2

Since n * p₀ , n * (1 - p₀) = 94.2  $\geq$ 10 , the sample size is greater than 5% of the population size, and the sample is given to be random , the requirements for testing the hypothesis are satisfied.