Quiz 13 ReviewName:

Standard(s) assessed / Score
16. Carrying out statistical tests
  • Carry out a test of significance (hypotheses, collect and organize data, compute test statistic, compute p-value, make decision, interpret in context)

17. Understanding Statistical Tests
  • Explain p-value as a probability
  • Understand the reasoning for a test of significance

Carrying out Statistical Tests

1.An auto dealer was listening one day to a radio talk show about car sales. A caller claimed that women select cars primarily on appearance characteristics, and that men select cars primarily on performance characteristics. The auto dealer wanted to determine if there was any validity to the caller’s claim. He decided to conduct a survey with the following question: What is the one characteristic of your present automobile that is most important to you?

I.Hypotheses

In the auto dealer’s study, what are the null and alternative hypotheses?

Ho:

Ha:

II.Data

The auto dealer conducted his survey based on a random sample. 200 men and 250 women responded. Of these, 81 men and 126 women gave an appearance characteristic, while the rest gave a performance characteristic.Organize the data into a two-way table.

Using the same totals in the table part II, fill in a new table with the expected cell counts under the assumption that the null hypothesis is true.

III.Test statistic

Compute the chi-square statistic. Show the substitution into the formula

IV.p-value

Use the table, calculator, or computer to find the p-value.

(Remember: The p-value is the probability of getting a sample result as or more extreme than the one observed assuming the null hypothesis is true.)

V.Decision

Make a conclusion based on your p-value as to whether or not to reject the null hypothesis. Circle one.

Reject HoFail to reject Ho

VI.State your conclusion in a sentence in the context of the problem.

2.Roberto suspects that one of the dice he uses to play Monopoly is biased. He rolls the die 100 times and gets 20 sixes.

a.What are the expected numbers of sixes and non-sixes for 100 rolls of a fair die?

b.Compute the chi-square statistic based on Roberto’s results compared to the expectation. Show your work.

c.Find the probability of getting 20 or more sixes in 100 rolls of a fair die. (In other words, find the p-value.)

d.What does this p-value suggest about Roberto’s belief that the die is biased?

Understanding Statistical Tests

3.Which of the following is not an explanation of the null hypothesis, Ho, in a statistical test.

(a) a statement of what we are trying to prove in an experiment

(b) it is usually a statement that the status quo holds or that “there is no difference”

(c) a neutral assumption made for the sake of argument

(d) it is the hypothesis that the researcher tries to disprove based on conflict with the observed data

4.A very small p-value indicates…

(a) that someone made a computational error

(b) strong evidence against the null hypothesis

(c) that the alternative hypothesis must be false

(d) that we should fail to reject the alternative hypothesis

5.Justin Timberlake claims that 25% of his fans prefer chocolate ice cream, 25% prefer vanilla, and 50% like dulce de leche best of all. If a random sample of 200 fans is selected and their preferences recorded, what is the expected number that will prefer each type of ice cream?

Suppose that the results from the sample differ from the expectation such that the p-value in a Chi-square test is 0.002. Which of the following is not a correct interpretation of this p-value?

(a) In only 2 random samples in a thousand would we see such a large difference between the observed and expected numbers of people preferring each flavor if JT is correct. Therefore, JT is probably wrong.

(b) There is only a .002 probability that a randomly selected fan would agree with JT

(c) The null hypothesis of the test is rejected at the .05 significance level

(d) If JT’s claim is true, the probability of observing such a large difference between the expected number of fans preferring each flavor based on JT’s claim and the actual number of fans preferring each flavor in a random sample of his fans is very small.

6.In a test of significance (or hypothesis test) we say that an observed difference is “statistically significant” if the observed data …

(a) shows a big enough difference to matter from a practical point of view

(b) would be unlikely to occur due to random variability

(c) demonstrates a difference large enough that it cannot reasonably be attributed to random sampling error (or random assignment of subjects to treatments in an experiment).

(d) both (b) and (c)