Central Limit Theorem Confidence Interval and Mortality Lab Report Introductory Statistic labs hwThere are lab7, lab8, lab9, and homework3Lab7 is primary.

Central Limit Theorem Confidence Interval and Mortality Lab Report Introductory Statistic labs hwThere are lab7, lab8, lab9, and homework3Lab7 is primary. Statistics, Lab #7
Central Limit Theorem Lab
Objective: To explore the
distribution of sample means.
Procedure: In a standard deck of
52 cards, assume each jack,
queen, and king takes on
numerical values of 11, 12, and
13, respectively. Use your
calculator to do the following
computations:
a. Compute the mean for the
entire set of 52 cards.
µ = _____
“Why can’t dogs play poker?” (Answer on the back.)
b. Compute the standard deviation for the entire set of 52 cards. s = _______
a. Construct a histogram for the entire set of 52 cards manually. Put the card face
values on the x-axis, and frequencies on the y-axis.
4
2
5
10
d. With a partner take the deck, shuffle and deal-out a hand with four cards. Average those
four cards
and list the averages in the table below. Do this a total of 40 times.
-2
10
-4
e. Repeat steps a, b, and c using your sample means (x-bars) from step d.
??!? = _______,??!? = _______, and histogram below. Remember that the histogram is done
from the STAT PLOT menu in the upper left-hand corner of the calculator keypad. Make
sure that your window corresponds to the grid below.
2.9
4.4
5.9
7.4
8.9
10.4
11.9
–
How do the two means in steps a and e compare? ____________________________
–
How do the two standard deviations from part b and e compare? Can you establish a
ratio as to how they compare to each other?
________________________________________________________________________
–
Describe the shape of the histogram from part e. How does it compare with the first
one?
_______________________________________________________________
–
If you were dealing hands with more than 4 cards (maybe 9), how would you think
that would change the following:
a. The shape of the histogram of the # ’s: _________________________________
b. The standard deviation of the ??? ’s: ____________________________________
Answer to the dog question in the previous page:
They can’t help but wag their tails when they get a good hand!
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Statistics Lab #8
Name: ____________
Confidence Interval Lab
Objective: To explore the meaning of “confidence interval” & “margin of error”.
Procedure:
a. Generate 5 random numbers from 1 – 100. This
may be done by using the following function:
rndInt(1,100,5). You need to first load MATH
menu, followed by PRB submenu. List these
five numbers:(Make sure there are no repeating
values) _________
b. Locate the five rectangles corresponding to the
above five numbers & list their areas:
______________
c. Average the five areas from b: _______
d. Repeat steps a-c three more times:________________
e. List the 4 averages in the first 7 lines of the table. Then work with others (or you
could this alone)until the columns that is titled “Averages” is completely filled in.
f. Next we would like to use an average (such as the one you found above) to
predict population average, probably by suggesting a range of values. Here we
go…
g. Let’s assume a sampling error of ±3, meaning add and subtract three to the
sample average.
Averages Interval
Does the interval Averages Interval
Does the interval
(Average + 3)
(Average + 3)
include the true
include the true
average*?
average*?
(yes or no?)
(yes or no?)
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Averages Interval
(Average + 3)
Does the interval
include the true
average*?
Averages Interval
(Average + 3)
(yes or no?)
Does the interval
include the true
average*?
(yes or no?)
* True average(??)=7.44
h. Next find out the proportion of class whose ranges include the population mean.
(You have to wait for me to tell you what that is… Just wait…)
Percent Inclusion: ____ that is how good the sampling error of 3 is.
i. How can we find a sampling error that is 95% good (confident)?
Don’t answer letter i. That’s is rhetorical question. Thx.
13
14
Statistics, Lab #9
Name: _________,_________
(print)
last
first
Mortality
Objective: Evaluating data and drawing conclusions
about life expectancy.
Motivation: Insurance agents know that the
premium or cost of an insurance policy is based
on the likelihood of a claim being filed. In the
case of life insurance, the insurance company is
making a bet that the client will survive. The
client is betting that they will not, in which case
a cash value will be forwarded to his or her
beneficiary. The fairness of the amount of the
premium and the value of the policy are all
based on mathematical statistics gathered from
large samples of individuals in what is called
mortality table. One of the earliest mortality
tables was compiled by Edmund Halley, for
whom the Comet is named, in 1693. The data in
mortality tables are used to make predictions
about the life spans of people who are still alive.
The Activity
According to mortality table the life expectancy for the general population is 80,
otherwise µ = 80.
Question: 1. What are your feelings about how the life expectancy locally (Bay Area)
compares with the national average. Explain.
_______________________________________________________________________
_______________________________________________________________________
Follow up question: 2. How do you think the above claim could be substantiated?
_______________________________________________________________________
3. Collect and list your data, use internet if you must, making sure that the gender is
identified in your sample: (Obviously more data you collect, your result will be better.
Make sure your data is not redundant. You should have at least 40 data values.)
15
4. For your data find the following: ??? = _____, ??! =______,
n = ____.
Conclusions:
5. According to CLT what is ??!? = ?_______
(Assume that sx = s.)
6. Use to scale the graph.
80
7. How many standard deviations (?#$ ) does your sample average falls from the
hypothesized mean (µ) of 80? ____________
8. Mark your sample average, , on the graph above. Is your sample outcome consistent
with the national average or does it support your claim? Explain.
_______________________________________________________________________
9. Would collecting all the data gathered by the class into a large pool enhance or
diminish the quality of the data? Explain.
_____________________________________________________
16
Homework 3(3 pages)
Name: _________,_________
(Print) last
first
1. In which of the following distributions is it appropriate to use normal approximation:
a. n = 222, P = 0.035
b. n = 189, P = 0.873
2. Use the continuity correction factor that describes the region of the normal curve that
corresponds to the indicated binomial probability.
a. The probability of fewer than 47 democrats.
d. P(x ? 79).
e. P(x > 46).
3. A drug manufacturer states that only 5% of the patients using a particular drug will
experience side effects. Doctors at a large university hospital use the drug in treating 250
patients. What is the probability that 15 or fewer of the 250 patients experience side effects?
a. Define x …
b. What are n and p…
c. CCF…
d. µ and s ?
e. Z-interval.
f. Probability?
12
4. A veterinarian has had many years of experience treating pet cats for a common kidney
infection. Based on experience the veterinarian knows that the mean time required to cure a
common kidney infection is 144 hours, with a standard deviation 57 hours. We are interested for
the average recovery time, based on a random sample of 45 cats.
a. What is µx ?
b. What is ? x ?
€
c. What is the shape of the distribution of the above sample means?
€
d. What is the probability that average recovery time for this sample is more than 160 hours?
e. What is the 85th percentile for the average recovery time for this sample of 45 cats?
5. To estimate the mean height of female high school juniors, you take a random sample of 30
female students and get these results (in inches):
72
51
67
68
61
69
58
56
60
56
66
61
60
59
59
54
58
53
68
63
57
62
63
64
56
62
58
67
57
70
a. What is your point estimated for µ? (hint: that would be ??? for the above sample.)
b. If s is 5.3, based on past research, find a 93% confidence interval.
2. How large a sample should be taken in the population mean is to be estimated with 88%
confidence to within $75? The population has a standard deviation of $900.
13
6. The drug Lipitor is meant to lower cholesterol levels. In a clinical trial of 863 patients who
received 10 mg doses of Lipitor daily, 47 reported a headache as a side effect. Construct an 86%
confidence interval for the population proportion of Lipitor users who will report a headache as a
side effect.
Z=?
E=?
CI : ?
7. A child psychologist wishes to estimate the percentage of fathers who watch their preschoolaged child when the mother works. What size sample should be obtained if she wishes the
estimate to be within 3 percentage points with 97% confidence if
a. She uses a 2015 estimate of 82% obtained from the U.S. Census Bureau?
Z=?
n=?
b. She does not use any prior estimates.
n=
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