Answer to Question #276622 in Statistics and Probability for yara

Question

 A student wants to see if the correct answers to multiple choice problems are evenly distributed. She heard a rumor that if you don't know the answer, you should always pick C. In a sample of 78 multiple-choice questions from prior tests and quizzes, the distribution of correct answers are given in the table below. In all of these questions, there were four options {A, B, C, D}.

Correct Answers (𝑛=78)

A B. C. D

Count. 10. 23. 10. 35

Test the claim that correct answers for all multiple-choice questions are not evenly distributed. Test this claim at the 0.10 significance level.

(a) Find the test statistic.

(b) Find the critical value.

Answer 1

n=78

the test is a chir-square test,

We from the data the observed means is denoted by O and the Expected means by E.

For us to get the Expected means we use the n=78 divide by the X= 4 ,(A,B,C,D) that is 19.5

The chir-square for the computed we sum up all the (O-E)^2/E .

a) X² =23.12798

b)from the table with 3 Degree of freedom the we get Chir-square value =6.251

Since 23.12798 is greater than 6.251 then we reject the null hypothesis.