Inference for Categorical Data: Proportions unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1 Paper 2 Paper 3

Each paper is built from this unit’s 59 terms and is the same for everyone, so a teacher can assign “Unit 3, Paper 1” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.

Suggested time 32 min 29 points0/17 attempted

p-value definition

Goodness-of-fit test

One-sided vs two-sided alternatives

Critical value z*

Degrees of freedom, goodness of fit

Chi-square statistic

Type I error rate

Why the interval does not pool

Conclusion wording

Why expected counts, not observed

Conditions for a one-proportion z-interval

Power

Short answer 1. Define or explain: Degrees of freedom, two-way tables

3 pts

Short answer 2. Define or explain: Significance level

3 pts

Short answer 3. Define or explain: Type II error

3 pts

Short answer 4. Define or explain: Conclusion template

3 pts

Free response

5 pts

A researcher wants to know whether preference among three brands of bottled water is associated with whether a taster is a regular bottled-water drinker. Independent random samples of 100 regular drinkers and 100 non-regular drinkers each tasted all three brands and named a favorite. The results are: Brand A Brand B Brand C Total Regular 45 30 25 100 Non-regular 30 40 30 100 Total 75 70 55 200

A. State the appropriate hypotheses and name the test.

B. Calculate the expected counts under the null hypothesis, and verify the conditions for the test.

C. Calculate the value of the test statistic and the degrees of freedom, and determine the p-value.

D. State your conclusion at the α = 0.05 level in the context of the study.