1. Other things being equal, which of the following p-values is best for the NULL hypothesis?
.1% 3% 17% 32%
2. True or false (and make sure you can explain):
a. The p-value of a test is the chance that the null hypothesis is true.
b. If the null hypothesis is right,
there is only a 1% chance of getting a z bigger than 2.33.
c. The probability of the null hypothesis given the data is 1%.
d. The p-value depends on the data.
e. If the p-value is 5%, there are 95 chances in 100 for the alternative
hypothesis to be right.
f. If the p-value is 43%, the null hypothesis looks plausible.
g. If z = 2.3, then the observed value is 2.3 SEs (standard errors)
above what is expected on the null hypothesis.
h. A p-value of 4.7% means something very different from a p-value of 5.2%.
i. The outcome of a hypothesis test is a p-value ranging between 0 and 1 which
describes the likelihood of the null hypothesis being true.
j. A highly statistically significant result cannot possibly be due to chance.
k. If a difference is highly statistically significant (ie, at alpha = .01),
there is less than a 1% chance for the null hypothesis to be right.
l. If a difference is highly statistically significant (ie, at alpha = .01),
there is better than a 99% chance for the alternative hypothesis to be right.
m. If a result is statistically significant (ie, at alpha = .05),
there are only 5 chances in 100 for it to be due to chance,
and 95 chances in 100 for it to be real.
n. A difference which is highly statistically significant must be very important.
o. A difference which is highly statistically significant can still be due to chance.
p. The p-value of a test depends on the sample size.
q. Data-snooping makes p-values hard to interpret.
3. Which of the following questions does a test of significance deal with?
a. Can the difference plausibly be explained by chance variability?
b. Is the difference important?
c. What does the difference prove?
d. Was the experiment properly designed?
4. A company has 7 male employees and 16 female employees. However, the men earn more on average than the women, and the company is accused of sex discrimination in setting salaries. An ‘expert witness’ reasons as follows:
There are 7*16 = 112 pairs of employees, where one is male and the second female. In 68 of these pairs, the man earns more. If there was no sex discrimination, the man would have only a 50-50 chance to earn more. That’s like coin tossing. In 112 tosses of a coin, the expected number of heads is 56, with an SE of about 5.3. So z = (68 – 56)/5.3 = 2.3, so the p-value is about 1%. That’s sex discrimination if I ever saw it.