Question

Suppose a teacher gives her statistics class a​ four-question, multiple-choice quiz at the beginning of the semester to measure how well prepared they were for the class. The accompanying table shows the number of students who had​ 0, 1,​ 2, 3 and 4 questions correct. Using α = 0.05, perform a​ chi-square test to determine if the number of correct answers per student follows the binomial probability distribution.

Number of Correct Answers per Student	Frequency
0	5
1	6
2	8
3	10
4	11

Total: 40

1. Calculate the test statistic.
x² = ____ (Round to two decimal places as needed.)

2. Determine the p-value for the test statistic.
p-value = ____ (Round to three decimal places as needed.)

3. State the appropriate conclusion:
(Do not reject/reject) H0. At the 5% significance level, there (is not/is) enough video evidence to conclude that the distribution of the number of correct answers per student does not follow the claimed, or expected, distribution.

Please be clear and concise with your response (so I will fully understand how the problem was solved)

Answer 1

Ans:

P(x=k)=4C_k*0.5^k*(1-0.5)^4-k

x	fo	p(x)	fe=40*p(x)	(fo-fe)^2/fe
0	5	0.0625	2.5	2.50
1	6	0.2500	10	1.60
2	8	0.3750	15	3.27
3	10	0.2500	10	0.00
4	11	0.0625	2.5	28.90
Total	40	1	40	36.27

Test statistic:

chi square=36.27

p-value=CHIDIST(36.27,4)=0.000

Reject H0.At the 5% significance level, there is enough video evidence to conclude that the distribution of the number of correct answers per student does not follow the claimed, or expected, distribution.