Question

Well help 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 56% of the students complete the course with a letter grade of A, B, or C. In the experimental course, of the 17 students enrolled, 13 completed the course with a letter grade of A, B, or C. Is the experimental course effective at the u=0.01 level of significance? Complete parts (a) through (g). (a) State the appropriate null and alternative hypotheses. H versus H, MMU (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) = 10, the normal model 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 number of trials with The trials independent and the probability of success is fixed at 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 Click to select your answer(s).

Answer 1

Given: 0.76 > o.S6 ca) H: Þ Ho: Ps 0.SG Vs 4.19 = 4.2 (b) nP. (1-P.) = 17 x 0, 56 X 0.4 Becaus e n Po(l-P.) <10 the normal model may not be used to P- v al ue approximate the There is fix ed number of tricus with two CO) The trials are mutu dlly exclusive outcomes, independent and the pro ba bility of success is fixed for each trial at 0.56 value 0.0475 Ed) do not reject the null hypothesis because the p-value is greater than x. There is insu fficient conclude that the experimenta course No evidence to is effective 39 ce) 0.765 npocI- Po) = 51X0.56 x o .44 : 12,6 the sample size is 51. of the population size and the ean be reasonably assumed to be random the normal model may be used to approximate the Because nP. Cl-Po) = 12.6 > 1o less th an sample þ- value

f-P. Po (1-Po) Test statistic, O. S6 O. 765 - O. S6 X0.44 51 0. 205 O. 0695 2.95 þ- value s 2- table) (from yes reject the null bypothesis because the p-value lesss than K. is evidence to There is sufficient conclude that the experimental course is effective there are cwhen small sample sizes, the in the null evidence against the statement hypetnesis must be insignificant. of studies that one should be do0'not réject was conducted wary null hypothesis when the small sample size the test with a