Week of January 4 In text : 1.15, 1.25, 1.55, 1.61 and

1.
The nine players chosen to start for the National League in the major league All Star game had the following batting averages:

.304 .321 .289 .307 .352 .284 .329 .306 .190

a)
What is the mean batting average for these starters?
b)
What is the standard deviation for the batting averages of the starters?
c)
An astute observer questions the inclusion of the pitcher (who has the . 190 average) in the calculation because pitchers are not paid to hit. If the pitcher is omitted, what is the batting average of the eight other starters and what is the standard deviation for them?
d)
Do you think that the batting average for the eight starters would be a good estimate for the population mean of all major league ballplayers? Would you expect the population mean to be larger or smaller? Why?
e)
Do you think that the standard deviation of the eight batting averages for the starters (excluding the pitcher) is a good estimate for the population standard deviation? Would you expect the population standard deviation to be larger or smaller? Why?
2.
Students are surveyed as to their number of close friends (individuals to whom they would not be afraid to confide a deep secret). The frequency distribution of replies is given below.



Number of friends (x)	f
0	2
1	3
2	5
3	5
4	4
5	1

a)
How many students were surveyed?
b)
Compute the relative frequencies and construct a histogram.
c)
What percentage of the students had 2 or fewer close friends?
d)
Find the median, mean and standard deviation.
3.
Columnist Ann Landers was asked whether having children was worth the problems involved. She asked her readers "If you had it to do over again, would you have children?" A few weeks later her column was headlined "Seventy Percent of Parents Say Kids Not Worth It", because 70% of the parents who wrote said they would not have children if they could make the choice again. Is this a valid conclusion? Comment.

Week of January 11 In text: 1.69, 1.71, 1.77, 1.79, 1.81, 1.87, 1.91, 1.95 and

1.
a)
In 1975 Governor Brown of California proposed that all state employ given a flat raise of $70 per month. What would this do to the mean monthly salary of state employees? to the standard deviation?
b)
What would a 5% increase in the salaries, across the board, do to the average monthly salary? to the standard deviation?
2.
100 dumpsites were tested for the presence of six toxic pollutants. The results are given below:
Number of pollutants found:

0

1

2

3

4

5

6


Number of dumpsites

2

28

25

22

11

9

3

a)
What was the mean number of pollutants found per dumpsite.
b)
If a dumpsite is chosen at random from the 100 sites, what is the probability that it has more than 3 pollutants? fewer than 2 pollutants? no pollutants?
c)
Construct a boxplot for these data. Are the data symmetric?
d)
Compare the mean and median for the dumpsite data. Are the results of this comparison supported by your conclusions in (c)?
e)
Compute the standard deviation. What proportion of the observations fall in the I interval ą 2s ?

1.
An optometrist claimed that the mean waiting time for her patients was at most 10 minutes. A sample of 16 patients showed an average waiting time of 12 minutes with a standard deviation of 4.4 minutes.
a)
Test the optometrist's claim. State null and alternative hypotheses, value of the test statistic, p-value and conclusion.
b)
For what values of a would the null hypothesis be rejected?

For what values of a would we fail to reject the claim?

c)
Calculate a 90% confidence interval for the mean waiting time.