Question

A national publication showed the following distribution of favorite class subjects for high school students.

Class Subject Math English Social Studies Physical Education Music Other
Percentage 5% 14% 28% 26% 20% 7%

Pasquale, a student from a high school of 1,200 students, wants to see whether the distribution at his school matches that of the publication. He stands at the school entrance in the morning and asks the first 40 students he sees what their favorite class is. Pasquale records the following table of observed values.

Class Subject Math English Social Studies Physical Education Music Other
Observed 7 8 7 6 6 6

He decides to conduct a chi-square goodness-of-fit test to see whether his high school's distribution differs significantly from that of the publication. Pasquale’s statistics teacher tells him that his information does not meet the conditions necessary for a goodness-of-fit test. Which condition has not been met?

Answer 1

1 and 111 only

Explanation:

The goodness of fit test is used to examine if there is significant evidence to say thatvthe observed and expected freqencies are from the desired distribution.

Condituis required for performing a goodness of fit test on a data include :

Randomness, sampled Data must have been chosen at random in other to be representative, here, randomness isn't exhibited as Pasquale used more of convenient sampling questioning the first 40 students.

Also, the expected value of the number of sample observation in each level of the variable should be atleast 5.

This is also violated, as the expected values for some of the levels are less than 5

Hence, conditions 1 and 111 are not met