Stat 200
Homework 9 Solutions
9.1 …Is this a fair die? Answer using a significance test with H
0
: p
i
= 1/6 for each i and
H
A
: p
i
≠ 1/6 for at least one i.
Solution
> rolls <- c(13, 17, 9, 17, 18, 26)
> die.prob <- rep((1/6), 6)
> die.prob
[1] 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667 0.1666667
> chisq.test(rolls, p=die.prob)
Chi-squared test for given probabilities
data: rolls
X-squared = 9.68, df = 5, p-value = 0.08483
The p-value of .08483 is not significant. Therefore, we accept the null hypothesis and
that we could not find sufficient evidence for the die being a biased die.
9.5 …Perform a chi-squared goodness-of-fit test to see whether the distibution of vowels
appears to be from English.
Solution
> count <- c(28, 39, 23, 22, 11)
> expected <- c(9, 12, 9, 8, 4)
> prob <- expected/sum(expected)
> chisq.test(count, p=prob)
Chi-squared test for given probabilities
data: count
X-squared = 1.084, df = 4, p-value = 0.8968
The p-value suggests that we do not reject the null hypothesis and that the paragraph
came from the English language.
9.7 The number of murders by day of week in New Jersey during 2003 is shown in Table
9.4. 1. Perform a significance test to test the null hypothesis that a murder is equally
likely to occur on any given day.
2. Perform a significance test of the null hypothesis that murders happen on each
weekday with equal probability; similarly on the weekends, but not necessarily
with the same probability.
For each test, write down explicitly the null and alternative hypotheses.
