Question

A business school professor uses multiple choice tests. Each question on his exams has five possible answers which are assumed to be equally likely. One of his brighter students wants to know whether this assumption is correct and whether or not this professor randomly distributes the correct answer over the five choices. If not, he believes he can improve his odds when guessing the answer to questions he is not sure of. The student took 1000 questions from previous tests and found the following distribution: a = 185, b = 230, c = 215, d = 180 and e = 190.
Required:
a. Formulate the null hypothesis for this test?
b. How many degrees of freedom do you have for this test?
c. What is the calculated value of the test statistic?

Answer 1

Answer:

a. The null hypothesis for this test is that the observed distribution is the same as uniform distribution

b. The degrees of freedom do you have for this test is 4

c.  The calculated value of the test statistic is 9.250

Step-by-step explanation:

a. According to the given data we can conclude that the null hypothesis for this test is that the observed distribution is the same as uniform distribution.

b. In order to calculate the degrees of freedom do you have for this test we would have to make the following calculation:

degrees of freedom=k-1

degrees of freedom=5-1

degrees of freedom=4

c. In order to calculate the value of the test statistic first we have to calculate the frecuency expected as follows:

expected frecuency=total observed frecuency/total number of category

expected frecuency=1,000/5

expected frecuency=200

Hence, to calculate the value of the test statistic we have to calculate the following formula:

x∧2=∑(fo-fe)∧2/fe

=(185-200)∧2/200+(230-200)∧2/200+(215-200)∧2/200+(180-200)∧2+(190-200)∧2

=9.250

The calculated value of the test statistic is 9.250