7120 Referring to Problem 754 find the least number of quest

7.120. Referring to Problem 7.54, find the least number of questions a student must answer correctly before the
instructor is sure at a significance level of (a) 0.05, (b) 0.01, (c) 0.001, (d) 0.06 that the student is not merely
guessing. Discuss the results.

Reference 7.54

(P/S: do not need to solve the problem 7.54)

Solution

No of questions -- 10

Prob of answering right just by guessing = 0.5

Let X be the no of right answers

X if guessed if binomial with p = 0.5 and n =10

P(X<7) = 0.828125

Let us assume that Mean = np (if guessed)

H0: mu = 5

Ha: mu < 5

Sample mean= a

Mean difference = 7-a

Std error = rt of npq = 0.5

Hence t statistic=(7-a)/0.5

df = 9

Hence no of correct answers should be

6.5417, 6.187, 5.805, 6.55

Rounding off we can say 7, 7, 6, and 7