4. A statistics instructor gave a four-quesiton true-false quiz to his class of

Question

4. A statistics instructor gave a four-quesiton true-false quiz to his class of 150 students. The results were as follon Number correct 012 34 71 35 Observed The 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 this null 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 0.05 level? (4 pts)

Explanation / Answer

H0 : The data follows binomial distribution.

H1 : The data does not follows binomial distribution.

Using excel:

To calculate the probability use: =BINOMDIST(x,4,0.5,FALSE). Find probability for x=0,1,2,3,4

Expected frequency = total frequency*prob = 150*prob

no_correct(x)

observed

prob

expected

0

2

0.0625

9.375

1

13

0.25

37.5

2

29

0.375

56.25

3

71

0.25

37.5

4

35

0.0625

9.375

To get the p-value for chi square test:

=CHITEST(actual_range, expected_range)

The p-value is 3.35404E-28

Since p-value < 0.05, we reject the null hypothesis at 5% level of significance and hence conclude that the data does not follow binomial distribution.

no_correct(x)

observed

prob

expected

0

2

0.0625

9.375

1

13

0.25

37.5

2

29

0.375

56.25

3

71

0.25

37.5

4

35

0.0625

9.375

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.