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Name: ________________________
Make-Up Test
Math 63 – Fall 2005
Instructions: You may work on this test alone or in a group of no more than 3 people. For a
group write all names on the top and show all work on one test. The score that you receive will
be averaged with your lowest midterm score with a weight of 2. If it is lower than your lowest
midterm score no averaging will be done (in other words this can’t hurt you it can only help you). You may
use your book and notes, but all work needs to be shown and appropriate formulas need to be
given and substituted into. For instance if I ask for the mean you may not just give the answer
from your calculator. I expect to be given the formula: x-bar = x/n and have the x given and n
given. The x can be from your calculator, but I want it written down.
1.
a)
Listed below are the weights of nine randomly chosen models (in pounds):
125, 119, 128, 128, 119, 127, 105, 123, 115
Find the following:
mean
b)
median
c)
mode
d)
midrange
e)
range
f)
variance
g)
standard deviation
h)
Q1
i)
Q2
j)
Q3
k)
Using the range rule of thumb what would you expect the standard deviation to
be? How does it compare with the actual standard deviation in part g)? Can you
make an inferences about the data based upon this comparison? If so, what
inference can be made. Note: This is not the value that is used for the standard deviation of
the sample if data is available.
l)
What is the level of measurement of this data? What does the level of measure
tell you about the validity of parts a) – j)? (Hint: If this were qualitative data would all
calculations be valid?)
m)
Construct a boxplot for the data.
n)
Construct a 98% confidence interval for the population mean of model weights.
o)
Construct a 98% confidence interval for the standard deviation of model weights.
p)
What is the probability of finding a group of 9 women in the general population
with an average weight less than the average weights of the models? The mean
weight is 143 lbs. and a standard deviation of the population is 29 lbs. (Hint: CLT)
q)
With a significance level of 0.02 test the claim that the average weight of the
general population is less than 143. Clearly state H0 and HA. (Note: We must assume
that they are from a normally dist. pop.)
r)
With a significance level of 0.01 test the claim that the weights of models vary
less than the weights of the general population. Clearly state H0 and HA. (Note:
We must assume that they are from a normally dist. pop.)
EC)
Considering the answers to last 2 questions does it seem reasonable that models
weights are not typical of the general population?
s)
Now, for the lowest models’ weight find the number of standard deviations from
the population mean. (Hint: Finding the z-score as if it is from the general population.)
Before hypothesis testing we would generally comment on whether these numbers were more than
2 standard deviations from the mean and comment that they were unusual based upon the values.
Note that with hypothesis testing we gained power of inference to make a general claim.
2.
Using the table on page 336 follow the following scenarios through and determine
the correct test statistic (t or z) to use for hypothesis testing in the following
scenarios.
a)
Graphical analysis reveals a skewed distribution of 200 sampled test
scores. The population parameters are completely unknown.
b)
c)
d)
3.
31 average test scores for students in Statistics courses are to be analyzed,
and it is known that the standard deviation of the population is 5.
15-IQ scores are chosen from the population. All IQ scores are known to
have a normal distribution with a known standard deviation.
A normal probability plot reveals an almost perfectly straight line in a
sample of 21 weights. Nothing is known about the original population.
The following boxplot shows heights (in inches) of a large collection of randomly
selected adult women.
71.1
56.1
62.2
a)
b)
c)
63.6
65.0
Assuming that this is a perfectly, symmetric distribution what would the
mean be?
If one of these women is randomly selected, find the probability that her height is
between 56.1 and 62.2 inches. (Hint: Use the quartile information)
If one of these women is randomly selected, find the probability that her height is
below 62.2 or above 63.6 inches.
d)
If two women are randomly selected, find the probability that they both have
heights between 62.2 and 63.6 inches. (Hint: Independent probabilities)
4.
In a recent survey, respondents were asked if they had a gun in their home. Of the
people asked 413 said they did, and 646 said that they did not or had no comment.
a)
What is the percentage of respondents that said they did have a gun in
their house?
b)
Construct a 95% confidence interval to estimate the percentage of the
population that would say that they have a gun in their house.
c)
Why would it be wrong to say that there is a 95% chance that the true
population proportion is in the range indicated by part b)? How can the
confidence interval be correctly interpreted. (Hint: See page 302)
d)
Test the hypothesis that less than 50% of the population has guns at a 0.05
confidence level.
e)
How do parts b) and d) relate to one another?