Question

say a student uses their personalized class data set to test the hypothesis that more than 50% of the people in class are in Chemistry, and rejects the null hypothesis at the 2% significance level. Consider the following statements. (i) The proportion of students in this class who are in Life Sciences is in fact greater than 50%. (ii) The p-value is greater than .02. (iii) The probability of Type II error is less than than 2%. (iv) A Type I error might have occurred. (v) If another student in this class tested the same hypothesis with their personalized class data set, using the same significance level, then that student might not reject the null hypothesis. Fing out which of the above statements are true (1) or false (2). (For example, if you think that the answers, in the above order, are True,False,False,True,False then you would enter '1,2,2,1,2' )

Answer 1

(i) The proportion of students in this class who are in Life Sciences in fact greater than 50% : FALSE

Note : The research hypothesis is : The proportion of students in this class who are in Life Sciences is greater than 50% .This is our alternative hypothesis . And our null hypothesis is ,H0:The proportion of students in this class who are in Life Sciences is not greater than 50%. On the basis of the test , we reject the null hypothesis and conclude that there is sufficient evidence to conclude that the proportion of students in this class who are in Life Sciences is greater than 50%. That means probability is more of alternative hypothesis being  true , but we are are not cent percent confident of that . Thus we cannot say that The proportion of students in this class who are in Life Sciences in fact greater than 50% .

(ii) The p-value is greater than 0.02 : FALSE

Note : Given significance level is 0.02 and also the students rejects the null hypothesis . The null hypothesis is rejected when P value is less than significance level. Thus P value cannot be Graether than 0.02 .

(iii) The probability of type II error is less than 2% . FALSE

Note : Type II error is the error of accepting a false null hypothesis. Given, the probability of type I error is 0.02 . We cant say , how much is probability  type II error. In general probability of I type I error is kept lower than probability type II error, as type I error is considered more serious than type II error. Thus probability of type II error cannot be less than 2% .

(iv) Type I error might have occurred .TRUE

Note : Type I error is the error of rejecting a true null hypothesis. As the student have rejected the null hypothesis, she might have committed type I error.

(v) The other student might not reject the null hypothesis. TRUE

Note : The first student rejects the null hypothesis . She cannot be cent percent sure that , her conclusion is true. There is 2% chance that her conclusion was wrong ( type I error) . Thus other student might not reject the null hypothesis.

Thus Anwser is 2,2,2,1,1