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Chi-square Goodness of Fit test

Consider the following problem:
A research firm claims that the distribution of the days of the week that people are most likely to order food for delivery is different from the distribution seen in the past. You randomly select 494 people and record which day of the week each is most likely to order food for delivery. The table below also shows the results of your count. At alpha, α, = 0.05, test the research firm’s claim.

This sounds like a test of Goodness of Fit between the historical pattern and the observed pattern.

The claim is that the actual pattern and the historical pattern are different. That means we need the inequality math operator, which, in turn, means the claim is the alternative hypothesis.

Stating our two hypotheses:Chi-square Goodness of Fit test

Example problem re: Goodness of Fit test:

You are given a six-faced die and asked to determine with 95% confidence if it is “fair.”

  • What are the hypotheses?

Answer: the null H0: the die is fair, p1 = p2 = … = p6 = 1/6; the alternative Ha: the die is not fair, at least one pi ≠ 1/6.

  • What is the critical value of chi-square?

Answer: degrees of freedom df = 6 – 1 = 5. From a table or calculator, χ0.052 =11.071.

Common student mistake #1:Example problem re: Goodness of Fit test:

The F-test using Excel

F-test
F-test Critical Area

I teach graduate statistics, otherwise known as quantitative methods/analytics. I have found a lot of good statistics tutorials on You Tube and have recommended some to my students. Because these students are MBA students and not Ph.D. students, I am more concerned with my students leaving the course knowing how to use technology to help them solve business problems than with their having an in-depth knowledge of statistical theory or memorizing equations. There are many technology tools, i.e. statistical software, available, some free and some expensive for an individual to buy. Fortunately, most MBA students become at least familiar with Excel during their MBA if they were not already familiar with it. Moreover, many, if not most, companies use The F-test using Excel