Adebate recently erupted about the optimal strategy for playing a game on the tv show called "let's make a deal." in one of the games on this show, the contestant would be given the choice of prizes behind three closed doors. a valuable prize was behind one door and worthless prizes were behind the other two doors. after the contestant selected a door, the host would open one of the two remaining doors to reveal one of the worthless prizes. then, before opening the selected door, the host would give the contestant the opportunity to switch his or her selection to the other door that had not been opened. the question is, should the contestant switch?

a. suppose a contestant is allowed to play this game 500 times, always picks door number 1, and never switches when given the option. if the valuable prize is equally likely to be behind each door at the beginning of each play, how many times would the contestant win the valuable prize? use simulation to answer this question. round your answer to a percentage.
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b. now suppose the contestant is allowed to play this game another 500 times. this time the player always selects door number 1 initially and switches when given the option. using simulation, how many times would the contestant win the valuable prize? round your answer to a percentage.
%

Listed below are time intervals (min) between eruptions of a geyser. assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. does it appear that the mean time interval has changed? is the conclusion affected by whether the significance level is 0.10 or 0.01? recent 78 90 90 79 57 101 62 87 71 87 81 84 57 80 74 103 62 past 88 89 93 94 65 85 85 92 87 91 89 91 follow the steps of hypothesis testing, including identifying the alternative and null hypothesis, calculating the test statistic, finding the p-value, and making a conclusions about the null hypothesis and a final conclusion that addresses the original claim. use a significance level of 0.10. is the conclusion affected by whether the significance level is 0.10 or 0.01? answer choices below: a) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.01 but is not rejected when the significance level is 0.10. b) no, the conclusion is not affected by the significance level because h0 is not rejected regardless of whether a significance level of 0.10 or 0.01 is used. c) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01. d) no, the conclusion is not affected by the significance level because h0 is rejected regardless of whether a significance level of 0.10 or 0.01 is used.