Download NAME: DATE: Algebra 2: Homework 15

NAME:
DATE:
Algebra 2: Homework 15-9
1. The three distributions below relate to the population of all of the random segment lengths and to
samples drawn from that population. The eight phrases below could be used to describe a whole
graph or a value on the graph. Identify where on the appropriate graph the phrases could be placed.
(For example, segment of length could be placed by any of the values in the column for on the
plot labeled Length.)
a. Random sample of size
of segment lengths
b. Segment of length
c.
Sample mean segment length of
d. Mean of sampling distribution,
e. Simulated distribution of sample means
f.
Sample segment lengths
g. Population of segment lengths
h. Mean of all segment lengths,
2. Two simulated sampling distributions of the mean segment lengths from random samples of size
are displayed below.
Distribution A
Distribution B
a. Compare the two distributions with respect to shape, center, and spread.
b. Distribution A has a mean of
, and Distribution B has a mean of
compare to the population mean of
?
c.
. How do these means
Both Distribution A and Distribution B have a standard deviation
. Make a statement about
the distribution of sample means that makes use of this standard deviation.
3. The population distribution of all the segment lengths is shown in the dot plot below. How does the
population distribution compare to the two simulated sampling distributions of the sample means in
Problem 2?
4. Which of the following will have the smallest standard deviation? Explain your reasoning.
A sampling distribution of sample means for samples of size:
a.
b.
c.
5. Explain the difference between the sample mean and the mean of the sampling distribution.
6. Say we are investigating the heights of 16 year old American males. Say we know that the population
mean height is 65.3 inches with a standard deviation of 4.2 inches. Let’s say we take a sample of 16 year
old American males. The sample has a size of 30.
a) Will the mean height of the sample always be
b) Will the standard deviation of the sample be 4.2
65.3? Why or why not? Could it be significantly
inches? Would you expect more or less variation
different?
in a sample versus a population?
REVIEW:
7. Howard collected fish eggs from a pond behind his house so he could determine whether sunlight had an effect
on how many of the eggs hatched. After he collected the eggs, he divided them into two tanks. He put both tanks
outside near the pond, and he covered one of the tanks with a box to block out all sunlight. State whether
Howard's investigation was an example of a controlled experiment, an observation, or a survey. Justify your
response.
8. Solve algebraically for all values of x: