1.) The table below shows the critical reading scores for 14 students the first two times they took a standardized test. At alphaαequals=?0.01, is there enough evidence to conclude that their scores improved the second time they took the? test? Assume the samples are random and? dependent, and the population is normally distributed.
Student: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
First test: 589, 418, 437, 612, 547, 579, 337, 463, 566, 535, 510, 547, 622, 394
Sec test: 594, 477, 493, 627, 526, 620, 325, 581, 646, 592, 546, 568, 634, 413
(b) Find the critical? value(s) and identify the rejection? region(s).
t0=______
(c) Calculate d and sd.
(d) Use the? t-test to find the standardized test statistic t.
2.) In a survey of 175 females who recently completed high? school, 76?% were enrolled in college. In a survey of 150males who recently completed high? school, 64?% were enrolled in college. At alpha equals α = 0.05?, can you reject the claim that there is no difference in the proportion of college enrollees between the two? groups? Assume the random samples are independent.
(b) Find the critical? value(s) and identify the rejection? region(s).
?(c) Find the standardized test statistic.