1) 2) The probability of getting a head from tossing a fair coin is 0.50, or 50%. If you are to toss the same coin twice, with a reasonable assumption that the tosses do not interfere with each other, the probability that you will get two heads in a row will be 0.50 x 0.50 = 0.25 = 25%. If you are to toss the same coin five times, the probability that you will get five heads in a row will be 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.03125 = 3.125%. To generalize, the probability of getting the same result in a row is given by: Probability of getting heads n times in a row = Probability (Head) x Probability (Head) x ... Probability (Head) a) In rolling a fair cubic dice, the chance of getting a number greater than 2 is approximating 0.6667 or 66.67%. If you are to roll the same dice three times, with a reasonable assumption that the tosses do not interfere with each other, what is the probability that you will get a number greater than 2 three times in a row? (3 pts) i. ii. b) Karen is going to conduct 7 experiments to test a psychological effect. Unknown to Karen, this psychological effect truly exists (i.e. Ha is true). In each of Karen's experiments, a is set at 5% and the experimental design always leads to a of 30%. Assume that the 7 experiments do not interfere with each other, what is the probability that Karen will get = Probability (Head) to the power of n = 0.5" Seven significant results in a row Commit type I error seven times in a row Study 1 Multiplied by n times. In an experiment, Lisa randomly assigned participants to recall a past experience of being socially excluded or socially included. She then measured their prosocial behavior. The null hypothesis is that there is no difference between the two groups. She adopted an a of 0.05 (two-tailed). The descriptive statistics are shown below. Exclusion Group SD 0.69 Mean 0.38 n 17 Inclusion Group Mean SD 1.42 0.88 (3 pts) (3 pts) n 17 a) Conduct an independent sample t-test and decide if the null hypothesis should be rejected. Show your calculation clearly. (10 pts)