30) IQ: Scores on a certain IQ test are known to have a mean of 100. A random sample of 60 students attend a series of coaching classes before taking the test. Let be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if > 100. A test is made of the hypotheses H0: = 100 versus H1: > 100. Consider three possible conclusions: (i) The classes are successful. (ii) The classes are not successful. (iii) The classes might not be successful. C) Assume that the classes are successful but the conclusion is reached that the classes might not be successful. Which type of error is this? D) Assume that the classes are not successful. Is it possible to make a Type I error? Explain E) Assume that the classes are not successful. Is it possible to make a Type II error? Explain. 38) Larger or smaller P-value? Juan and Mary want to test the null hypothesis that the mean length of text messages sent by students at their school is 10 characters versus the alternative that it is less. Juan samples 100 text messages and finds the mean length to be 8.4 characters. Mary samples 100 messages and finds the mean length to be 7.3 characters. Both Juan and Mary obtained the same standard deviation. Will Juan's P-value be greater than, less than, or the same as Mary's P-value? Explain. *Please show all the work and be organized with your answers*