STAT 205 HW6
Due November 18
Note: Please ignore the sample size requirements for these problems – you may use the relevant formulas even if the sample sizes are technically too small.
1.
The average skill level in a population of chess players is 546 (on a scale of 1-1000) with a standard deviation of 100. A chess player named Owen played 25 games against randomly selected opponents, and the average skill level of those opponents was 612. Owen believes that he was the victim of bad luck, as this average was higher than expected. Use the central limit theorem to find the probability that the average skill level of Owen’s opponents was at least 612. Would you agree that the player was the victim of bad luck?
2.
In the upcoming political election, 50 voters were surveyed as to whether or not they support a candidate, with 26 voters expressing support for the candidate and the rest not expressing support for the candidate. a.
At a 95% confidence level, find the margin of error for the proportion of voters who support the candidate.
b.
At 90% confidence level, find the margin of error for the proportion of voters who support the candidate.
c.
Can the claim that at least 50% of voters support the candidate be supported?
3.
A sample of grade point averages was recently taken from a group of individuals who recently passed the California Bar Exam. The results were: 3.06, 3.56, 3.20, 2.87, 3.3, 3.61, 3.75, 3.1, 4, 3.65.
a.
Find the sample mean and sample standard deviation for these results.
b.
Find the 95% confidence interval for the mean G.P.A. of students who pass the California Bar Exam.
c.
Suppose that another sample was taken of 30 people who recently passed the California
Bar Exam, and the mean and standard deviation for the G.P.A.s in this group were the same as those that you calculated in part (a) above. Find the 95% confidence interval for
the mean G.P.A. of students who pass the California Bar Exam.
