One of two biased coins A and B is selected and flipped 3 times. Let A be the event that coin A is selected and B be the event that coin B is selected, with probabilities P(A) = 0.2 and p(B) = 0.8.
When coin A is flipped, the probability of heads is 0.9.
When coin B is flipped, the probability of heads is 0.5.
Let HHH be the event that the selected coin comes up heads 3 times. Complete the values X, Y, and Z in
Bayes' Theorem to determine the probability coin B was chosen if all 3 flips come up heads.
p(B|HHH)
Ex: 0.123
282) - 0.8
Ex: 0.123
-0.8 + Ex: 0.125
Y
Z
- 0.2

On a certain portion of an experiment, a statistical test result yielded a p-value of 0.21. what can you conclude? 2(0.21) = 0.42 < 0.5; the test is not statistically significant. if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time, so the test is not statistically significant. 0.21 > 0.05; the test is statistically significant. if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 79% of the time, so the test is not statistically significant. p = 1 - 0.21 = 0.79 > 0.05; the test is statistically significant.