Question: The administration of Saint Patrick’s College wants to lease space to a fast food franchise in its planned student center. Five national chains are interested, and each is known for its specialty product: burgers, fried chicken, pizza, sub sandwiches, or tacos. Senior management on campus presumes that all five choices would be equally appealing to college undergrads. The Student Life Office staff randomly samples 80 students to confirm student preferences, with students being allowed to make only one choice from among the cited five options. These are the observations they collected.

Is there sufficient evidence, at the 10% level of significance, to dispute the claim by the senior management of Saint Patrick’s College that all five choices for a fast food franchise in the new student center are preferred equally by its student body?

When solving non-parametric or distribution-free hypothesis testing problems, be sure to address all items from the following prompts:

1. Identify the non-parametric or distribution-free scenario that best models the problem context.
2. What are the null and alternative hypotheses, stated concisely with proper symbols if any?
3. What type of hypothesis test is involved: two-tail, one-tail left, or one-tail right? Explain.
4. Which type of test statistic is required, if any (e.g., z, or t or \({{\chi }^{2}}\) ) ? Explain.
5. Determine the critical value(s) that designate the rejection region(s). Indicate the critical value(s) from on an appropriate probability distribution (e.g., z, or t or \({{\chi }^{2}}\) ) or table of values.
6. Determine the value of the test statistic. Explain.
7. Determine the p-value that corresponds to the test statistic, if possible, for bonus credit. Explain.
8. Concisely state the technical conclusion using appropriate and complete statistical language.
9. Interpret the findings in complete thoughts/phrases and within the context of the problem.

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