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, 49% of the students complete the course with a letter grade of A, B, or C. In the experimental course, of the 18 students enrolled, 11 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the a = 0.05 level of significance? Complete parts (a) through (g). (a) State the appropriate null and alternative hypotheses. = |0.49 versus H,: > 0.49 Но: (Type integers or decimals. Do not round.) (b) Verify that the normal model may not be used to estimate the P-value. Because npo (1-P) = 4.5 < 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 independent and the probability of success is fixed at are 0.49 for each trial. (Type an integer or a decimal. Do not round.) (d) Determine the P-value using the binomial probability distribution. State your conclusion to the hypothesis test. First determine the P-value. P-value = 0.214 (Round to three decimal places as needed.) Is there sufficient evidence to support the research that the experimental course is effective? O A. 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. O B. 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. O C. 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. O D. No, do not reject the null hypothesis because the P-value is greater than a. There is insufficient evidence to conclude that the experimental course is effective 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, 49% of the students complete the course with a letter grade of A, B, or C. In the experimental course, of the 18 students enrolled, 11 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the a= 0.05 level of significance? Complete parts (a) through (g). O D. No, do not reject the null hypothesis because the P-value is greater than a. There is insufficient evidence to conclude that the experimental course is effective. (e) Suppose the course is taught with 54 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 npo (1- Po) =| V 10, the sample size is 5% of the population size, and the sample the normal model V be used to approximate the P-value. (Round to one decimal place as needed.) (f) Use the normal model to obtain and interpret the P-value. State your conclusion to the hypothesis test. First find the test statistic, zn. Zo = (Round to two decimal places as needed.) Now 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? Yes, reject the null hypothesis because the P-value less than a. There is sufficient evidence to conclude that the experimental course is effective. O B. Yes, reject the null hypothesis because the P-value is greater than a. There is sufficient evidence to conclude that the experimental course is effective. OC. No, do not reject the null hypothesis because the P-value is greater than a. There is insufficient evidence to conclude that the experimental course is effective. O D. No, do not reject the null hypothesis because the P-value is less than a. There is insufficient evidence to conclude that the experimental course is effective. (g) Explain the role that sample size plays in the ability to reject statements in the null hypothesis. When there are small sample sizes, the evidence against the statement in the null hypothesis must be One should be wary of studies that V the null hypothesis when the test was conducted with a small sample size.

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