Mathematical proof: the following mathematical proof has been designed so you trust this game. it proves that, when you click the 'play' button, we display the true winning number and don't make it up. the winning number is included (encrypted) in the number 'a' as explained below. the basic formula: a = b × c the number 'a' is displayed below. the numbers 'b' and 'c' will be displayed when you click the 'play' button. the numbers 'b' and 'c' are prime numbers. therefore, both of them are unique for any specific 'a'. the number 'b' is the lowest between 'b' and 'c'. data associated with the winning number winning number: the 2nd to 6th digits of the number 'b'. the number 'a': a.=.1599803588331327720483807275359 36958906748980572530395382385232029 10043626040901853730290446259523084 10717208773542546701902716118563586 76602322355049519296900625577993339 33289956380023871659348817998314025 83378981894882464234821265949271211 28318068741358281664229958072473312 64336182573490348327311227902700213 75389019177891404769157799880973219 80952222152990143538290760286049979 15280065916435760355090220459492787 56908870779183814044887212820901288 21805056072418863077895295039183925 42322668262689923117591772495942588 66501056868231059147583096069279497 39841027021193977527279184642104203 27492082099513316718236999756250466 67701421034893348173181940663921593 87230932872292719794716872286842039 4387

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.