7711 Homework – Kechris Lecture 9/10/15
1. The _________ hypothesis says that the sample difference is just due to chance; the _________
hypothesis says that the sample difference points to a real difference. Fill in the blanks.
Options: null, alternative
2. True or False:
a. If the p-value is 0.43, the null hypothesis looks plausible.
b. If the p-value is 0.43 of 1%, the null hypothesis looks implausible.
3. True or False and explain
a. The p-value of a test equals its observed significance level.
b. The alternative hypothesis is another way of explaining the results; it says the difference is due to
chance.
4. National data show that on the average, college freshman spend 7.5 hours a week going to parties. One
administrator does not believe that these figures apply at her college, which has nearly 3,000 freshmen.
She takes a simple random sample of 100 freshmen and interviews them. On average, they report 6.6
hours a week going to parties and the SD is 9 hours. Is the difference between 6.6 and 7.5 real? Begin
your answer by formulating the null and alternative hypotheses.
5. True or False and explain
a. The p-value of a test is the chance that the null hypothesis is true.
b. If a result is statistically significant at a 0.05 level, there are only 5 chances in 100 for it to be due
to chance, and 95 chances in 100 for it to be real.
c. A difference which is highly significant must be important.
6. One hundred investigators each set out to test a different null hypothesis. Unknown to them, all the null
hypotheses happen to be true. Investigator #1 gets a p-value of 0.55, investigator #2 gets a p-value of
0.08, and so forth. How many investigators should get a statistically significant result (at the 0.05 level)?
7. Other things being equal, which is stronger evidence for the null hypothesis: p-value = 0.03 or p-value =
0.27?
8. True or False and explain
a. A difference which is highly significant can still be due to chance.
b. A statistically significant number is big and important.
c. A p-value of 0.047 means something quite different than a p-value of 0.052.
9. Which of the following questions does a test of significance deal with
a. Is the difference due to chance?
b. Is the difference important?
c. What does the difference prove?
d. Was the experiment properly designed?
Explain briefly.
10. The five planets known to the ancient world may be divided into two groups: the inner planets (Mercury
and Venus), which are closer to the Sun than the Earth; and the outer planets (Mars, Jupiter and Saturn),
which are farther from the Sun. The densities of these plants are below; the density of Earth is taken as 1.
Mercury
0.68
Venus
0.94
Mars
0.71
Jupiter
0.24
Saturn
0.12
The two inner planets have an average density of 0.81, while the average density for the three outer
planets is 0.36. Is the difference statistically significant? Or does the question make sense?