Question

A genetic theory says that a cross between two pink flowering plants will produce red flowering plants 25% of the time. To test the theory, 100 crosses are made and 34 of them produce a red flowering plant. Is this strong evidence that the theory is wrong? Carry out the appropriate hypothesis test at the 5% significance level. The appropriate hypothesis for this test is O Ho: x = 0.25 vs. Ha: x = 0.25 O Ho: P = 0.25 vs. HA: P = 0.25 O Hp: = 0.25 vs. HA: H + 0.25 Ho: P = 0.25 vs. HA: P = 0.25 The test statistic is 40 (to two places after decimal) the p-value is 49) (to three places after decimal) There - enough statistical evidence to conclude that the theory is wrong. A study was conducted to examine the impact of speaking in public on college students. A class of 15 statistics students participated in the study. At the beginning of a lecture the students recorded their systolic blood pressure. During the lecture the instructor called on each student to stand and answer questions about topics in the lecture. After speaking the students once again recorded their blood pressure. The resulting values are given below along with summary statistics. before after difference 110 141 -31 123 142 -19 128 146 -18 125 136 -11 136 144 -8 108 111 -3 130 132 -2 113 114 -1 105 103 2 136 133 3 146 140 6 138 130 8 108149132 100 133 113 8 16 / 19 after mean before 125.8 14.27 127.9 15.45 difference -2.1 13.56 st dev Does this information indicate that blood pressure increased because of speaking? Conduct an appropriate hypothesis test and show appropriate steps. Let Hy mean systolic blood pressure before speaking in public, and H2 mean systolic blood pressure after speaking in public. The hypothesis for this test are: O Ho: M1 = H2 vs. HA: M1 < Hz or Ho: Md = 0 vs. HA: Md < 0 O Ho: 41 = M2 vs. HA: M1 > M2 or Ho: Hd = 0 vs. HA: Md > 0 O Ho: Mi = H2 vs. HA: M1 # Hz or Ho: Hd = 0 vs. HA: Md = 0 Fill in the blank: This is a two sample - t-test. The statistic for this test is t = 4.97 (to three places after the decimal), and the p-value is 49) (to three places after the decimal), There - sufficient statistical evidence, at the 5% level, to indicate that blood pressure increased because of public speaking.