Question

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? Data are collected using a random sample or randomized experiment n≤0.10N All expected counts are greater than 5.

Answer 1

The condition for a chi-square goodness-of-fit test that Pasquale's data may not meet could be non-random sampling, an insufficiently small sample size relative to the population, or expected frequencies less than 5.

Step-by-step explanation:

The student’s high school does not meet the conditions necessary for a chi-square goodness-of-fit test likely because one of the conditions mentioned has not been met. Given that the teacher’s response did not specify which condition is not met, we must consider all possibilities:

• Data are collected using a random sample or randomized experiment.
• The condition where n (sample size) must be less than or equal to 10% of N (population size), which is expressed as n≤0.10N.
• All expected counts are greater than 5.

If Pasquale’s data fail to meet any of these conditions, it would not be suitable to perform a chi-square goodness-of-fit test. Possible issues could include non-random sampling, having a sample size that is too large relative to the population size, or having expected frequencies less than 5, which could lead to inaccuracies in the chi-square approximation.