Download Section 7.2I sampling distribution of the sample mean

Section 7.2 Sampling Distribution of the Sample Mean
Statistics
Problems from 437 to 439 of text.
P7.) The distribution of the population of the number of motor vehicles per
household and sampling distributions of the mean for samples of size 4 and
10 are shown in Display 7.28 on page 437.
a.) Which distribution is which?
b.) The mean of the population is about 1.7. Theoretically, what is the mean
of the sampling distribution for samples of size:
4?
10?
c.) The standard deviation of the population is about 1. Theoretically, what
is the SE of the sampling distribution for samples of
size 4?
size 10?
P8.) From 1910 through 1919, the single-season batting averages of individual
Major League Baseball players had a distribution that was approximately
normal, with mean 0.266 and standard deviation 0.037. Suppose you
construct the sampling distribution of the mean batting average for random
samples of 15 players. What are the shape, mean, and standard error of this
distribution?
Shape is:
Mean is:
Standard error is:
P9.) Refer to the table below. Suppose a television network selects a random
sample of 1000 families in the US for a survey on TV viewing habits.
Number of
Children
0
1
2
3
4 (or more)
TOTAL
Number of
Families
53
20
17
7
3
100
a.) Describe the distribution of the possible values of the average number of
children per family.
b.) What average numbers of children are reasonably likely?
c.) What is the probability that the average number of children per family
will be 0.8 or less?
P10.) Last January 1, Jenny thought about buying individual stocks. Over the next
year, the mean of the percentage increases in individual stock prices is 6.5%
and the standard deviation of these percentage increases is 12.8%. The
distribution of price increases is approximately normal.
a.) If Jenny had picked one stock at random, what is the probability that it
would have gone down in price?
b.) If Jenny had picked four stocks at random, what is the probability that
their mean percentage increase would be negative?
c.) If Jenny had picked eight stocks at random, what is the probability that
their mean percentage increase would be between 8% and 10%?
d.) If Jenny had picked eight stocks at random, what mean percentage
changes in price are reasonably likely? (In other words, find the interval
that contains the middle 95% of possible mean percentage increases in
value.)
P13.) The distribution of the number of motor vehicles per household in the US is
roughly symmetric, with mean 1.7 and standard deviation 1.0.
a.) If you pick 15 households at random, what is the probability that they
have at least 30 motor vehicles among them?
b.) If you pick 20 households at random, what is the probability that they
have between 25 and 30 motor vehicles among them?
P14.) Refer to the table below. Suppose a television network selects a random
sample of 1000 families in the US for a survey on TV viewing habits.
Number of
Children
0
1
2
3
4 (or more)
TOTAL
Number of
Families
53
20
17
7
3
100
a.) Do you think it is reasonably likely that a sample of 1000 households
will produce at least 1000 children? Explain you reasoning.
b.) If the network changes to a random sample of 1200 households, does
this dramatically improve the chances of seeing at least 1000 children
in the sampled households? Explain.