Question

SAT coaching: A sample of 10 students took a class designed to improve their SAT math scores. Following are their scores before and after the class. Can you conclude that the mean increase in scores is less than 15 points? Let u, represent the mean score after the class and Mg = H, -M2. Use the a=0.10 level and the P-value method with the TI-84 Plus calculator. allo Before 470 473 443 459 Score 426 493 428 525 382 473 408 433 After 489 473 448 473 382 474 407 434 Send data to Excel Part 1 of 4 (a) State the appropriate null and alternate hypotheses. H: H - 15 <15 This is a left-tailed test. Part: 1 / 4 Part 2 of 4 (b) Compute the P-value. Round the answer to at least four decimal places. P-value = 0.3377

Answer 1

Giron. vs a) Md =15 This is a left tailed test Since this is a paired sample from Normal dist We know that Test statistie ir D = 10 2 Md Ntni Solan 10 After - before from data 1 = 19 os 14 2 32 01-11 P z 7.3 so = JED? - no A- 10.95 7.3-15 - 2.2237 fif 2.2237 10.95/10 so at at 164o devel table bal of tg is 1.383 So test statistics is 2.2237 so because of normal Cure nality we have 212237 - 2.225. 1 2,2237

table val, So test statistic is greater than so we conclude that we have suffient evidence to reject to pctgc 2,2237) = so pltg (2.262) = 0.025 pltg L1,833) -0.05 x = 2, 2237 fim) ? 2. = 1.833 fim, = 0.05 22 & 2.262 Flm2) -0.025 n-a fin) - fime 12-24 fim,) - fimi) 202237- 1.833 fim = 0.05 0.025-oos 2.262 - 1933 fro= 0.0272 hence the p-value is given by 0.0272