# Chi-Squared Goodness of Fit Hypothesis Test

Directions: Use the printouts to answer the following questions.

a) Write the null and alternative hypothesis. Include relationship implications. Assume the same

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proportions for the null.

b) Check the assumptions for a Goodness of Fit test. See the notes below.

Notes:

1. Assume that we have a census.

2. Assume we have a StatKey Chi-Square Goodness-of-Fit randomization dotplot.

3. Consider whether independence is met or not given our census in this situation.

c) What is the Chi-squared test statistic? Write a sentence to explain the test statistic.

d) Did the Chi-squared test statistic fall in the tail determined by the critical value?

e) Does the sample data significantly disagree with the null hypothesis? Explain your answer.

f) What was the P-value? Write a sentence to explain the P-value. Is there significant evidence?

g) Use the P-value and significance level to determine if the sample data could have occurred by random

chance (sampling variability) or is it unlikely to random chance? Explain your answer.

h) Should we reject the null hypothesis or fail to reject the null hypothesis? Explain your answer.

i) Write a conclusion for the hypothesis test. Explain your conclusion in plain language.

j) Is the population proportion related to the categorical variable or not? Explain your answer.

The Scenario: It is a big job to write and grade the AP-statistics exam for high school students each year. It is a difficult

multiple-choice exam. All questions have five possible answers A-E. Use a 5% significance level to test

the claim that percent of A answers is the same as the percent of B answers which is the same as C, D

and E. This would indicate that the letter of the answer is not related to the percentage of times it

happens.

Generated Samples = 6000

Sample Size = 400

Chi-Squared Statistic = 3.426

Critical Value = 10.125

P-Value = 0.495

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