Before looking at these solutions, please work the practice quiz.
Disclaimer: This quiz is representative of the level of difficulty you should expect, but it doesn’t include every single topic from the week’s work. The real quiz may include some other topics and may skip some that are in this practice quiz. (The real quiz also may not word questions in the same way as the practice quiz. You should focus on the concepts, not a particular form of words.)
See also: How to Take a Math Test
These solutions show about the same level of work I expect from you, though I often add some extra commentary. Please see Show Your Work for the what, why, and how.
See also: Top Ten Mistakes of Hypothesis Tests
Solution: This is attribute data, one population, more than two responses: Case 6, goodnesss-of-fit. There are 6 categories, therefore 5 degrees of freedom.
H0: The 25:25:20:15:8:7 model for ice cream preference is good.
H1: The 25:25:20:15:8:7 model for ice cream preference is bad.
|(2)||α = 0.05|
|(3–4)|| Use MATH200A Program part 6. Here are the input and output
You will write something like MATH200A/GOF and then the values: χ²=9.68, df=5, pval = 0.0849
Common mistake: When a model is given in percentages, some students like to convert the observed numbers to percentages. Never do this! The observed numbers are always actual counts and their total is always the actual sample size.
Alternative solution: You could give the model as decimals, .25, .20, .15 and so on. But for the model, all that matters is the relative size of each category to the others, so it’s simpler to use whole-number ratios.
Common mistake: If you do convert the percentages to decimals, remember that 8% and 7% are 0.08 and 0.07, not 0.8 and 0.7.
|(RC)||L3 shows the expected values, and they are all >5. The problem says that the 1000 people were a random sample.|
|(5)||p>α; fail to reject H0.|
|(6)|| At the 0.05 level of significance,
you can’t say whether the model is good or bad.
Remark: For Case 6 only, you could write your non-conclusion as something like “the model is not inconsistent with the data” or “the data don’t disprove the model.”
Remark: Note that the χ² test keeps you from jumping to false conclusions. Eyeballing the observed and expected numbers (L2 and L3), you might think they’re fairly far off and the model must be wrong. Yet the test gives a largish p-value.
Remark: If it had gone the other way — if p was less than α — you would say something like “At the .05 level of significance, the model is inconsistent with the data” or “the data disprove the model” or simply “the model is wrong”.
2(points: 7) Democrats and Republicans were surveyed for their opinions on gun control, and the results are shown in the table at right. Based on this sample, does a person’s opinion on gun control depend on party affiliation, at the .05 level of significance?
Solution: Use Case 7, 2-way table.
|(1)|| H0: Gun opinion is independent of party
H1: Gun opinion depends on party
|(2)||α = .05|
|(3–4)||Put the two rows and three columns in matrix A. (Don’t enter the totals.) Select χ²-Test from the menu. Outputs are χ² = 26.13, df = 2, p = 2.1181E-6 or 0.000 002 or <.0001.|
|(RC)|| Check the B matrix and verify that all expected
values are well above the minimum of 5.
Alternative: use MATH200A part 7 for steps 3–4 and RC.
|(5)||p < α; reject H0 and accept H1.|
|(6)||At the .05 level of significance, gun opinion depends on party.|
3(points: 1) 425 school children were surveyed about what they want to be when they grow up, out of a choice of five professions. The results were Teacher 80, Doctor 105, Lawyer 70, Police officer 70, Firefighter 100.
Obviously these particular children preferred some occupations over others. You want to test whether their preferences reflect a real difference in the population. What model do you use? (Write only the model; don’t do a hypothesis test.)
Alternative solution: Any other set of five equal numbers would be correct.