(b) Compute the P- value.(c) Determine whether to reject H0(d)State a conclusion A statistics instructor gave a four-question true-false quiz to his class of 85 students. The results were as follows.Number correct 0ObservedSend data to ExcelPart: 0 / 417 11Part 1 of 42337 204The instructor thinks that the students may have answered the questions by guessing, so that the probability that any given answer is correct is 0.5. Under thisnull hypothesis, the number of correct answers has a binomial distribution with 4 trials and success probability 0.5. Perform a chi-square test of this hypothesis.Can you reject Ho at the a= 0.01 level? Use the P-value method with the TI-84 Plus calculator.10(a) State the null and alternate hypotheses.Ho: The number of correct answers (Choose one)H₁: The number of correct answers (Choose one)binomial distribution with 4 trials and success probability 0.5.a binomial distribution with 4 trials and success probability 0.5.

The question is about is about categorical data analysis Given : To find : a ) Null and alt. hypo. b ) p value c ) Decision d ) ConclusionFirstly need to find prob. of using binomial dist. P ( X = x ) = n !x ! * ( n - x ) ! * px * ( 1 - p )n-x Here, trials ( n ) = 4, success prob. ( p ) = 0.5 P ( X = 0 ) = 4 !0 ! * ( 4 - 0 ) ! * ( 0.5 )0 * ( 1 - 0.5 )4 = 0.0625 P ( X = 1 ) = 4 !1 ! * ( 4 - 1 ) * ( 0.5 )1 * ( 1 - 0.5 )3 = 0.25 P ( X = 2 ) = 4 !2 ! * ( 4 - 2 ) ! * ( 0.5 )2 * ( 1 - 0.5 )2 = 0.375P ( X = 3 ) = 4 !3 ! * ( 4 - 3 ) ! * ( 0.5 )3 * ( 1 - 0.5 )1 = 0.25P ( X = 4 ) = 4 !4 ! * ( 4 - 4 ) ! * ( 0.5 )4 * ( 1 - 0.5 )0 = 0.0625 Then, Ei = n * Pi Where, n = ∑ Oi = 7 + 11 + 37 + 20 + 10 = 85 To find : Expected frequencies E1 = 85 * 0.0625 = 5.3125 E2 = 85 * 0.25 = 21.25 E3 = 85 * 0.375 = 31.875 E4 = 85 * 0.25 = 21.25 E5 = 85 * 0.0625 a ) Null and alt. hypo : H0 : The no. of correct answer answers has a binomial dist. with 4 trials and success prob. 0.5 H1 : The no. of correct answer answers does not have a binomial dist. with 4 trials and success prob. 0.5 b ) df= no. of expected values - 1 = 5 - 1 = 4 Using TI-84 Calculator i ) Go to STAT -- > EDIT -- > 1. Edit ii ) Enter the values observed data into list L1 and expected frequencies into list L2 iii ) Press STAT -- > TESTS -- > D. χ2 GOF Test iv ) Enter value as Observed : L1 Expected : L2 df : 4 Press Enter It provides output as χ2 = 10.51372549 p = 0.0326084493 p is nothing but the p value p value = 0.0326084493 c ) Decision rule : If p value < level of signif. ( α ) then reject H0 otherwise fail to reject H0 Given : level of signif. ( α ) = 0.01 Here, p value > α Hence, fail to reject H0 d ) Conclusion : There is insuff. evid to reject that the no. of correct answers has a binomial dist. with 4 trials and success prob. 0.5