ECON 4050 – Take-Home Quiz
NAME: Justin Dogan GRADE:____________________/35
This quiz is due at the beginning of class on Tuesday, Aug 29. You should work on your own on
this assignment. Note that the work comes directly out of Introduction to Statistics. If you have
difficulty with the material, please review your notes from Intro to Stats or reference an Intro to
Stats level textbook.
If you need additional materials, please check out a copy of any principles of statistics or
introduction to statistics textbooks from the Clemson library. Search for the sections on sample
averages, population means, sampling distributions, confidence intervals and hypothesis testing.
You may want to take a look at the Khan Academy videos on probability and statistics https://www.khanacademy.org/math/statistics-probability/ap-statistics.
IMPORTANT: Your work should be neat and professional (either typed or written neatly in pen).
Feel free to adjust the spaces in the Word document as needed to accommodate your answers. You
are not limited to the space that I have provided in the Word document: You can add more space or
delete rows to make your answers fit well.
I have made individual datasets for each of you. Open the attached Excel file ‘Quiz Data.’ On the
side column I have included the e-mails address for each student in the class alphabetically. To
answer the questions use your unique row of data. Your data is the column of data under your
name. If you can’t find your name (you joined the class after August 29), go to the last column titled
‘Extra,’ and use this row of data.
Please submit your answers directly into Canvas.
1. Record your 37 observations here:
108.612
110.844
115.330
105.518
114.188
108.977
98.680
106.358
104.474
98.215
109.332
108.967
105.880
99.223
112.553
97.802
101.926
108.855
100.069
105.044
101.834
105.562
103.865
110.996
116.528
110.753
115.438
106.286
106.939
109.333
103.456
113.806
115.762
98.851
110.127
107.473
99.166
2. Draw/insert a histogram of the data. You can either draw the histogram very neatly, or you may
use Excel or another statistical program to draw it for you. (3)
3. Based on this histogram, what is the likely distribution of the population? What in the histogram
leads you to this conjecture? (2)
Skewed to the right, the median is slightly to the left of the center.
4. What is the sample average? Show the formula and your calculations. (2)
Sample mean=106.9465078
Calculated in excel: take the sum of observations and divide by the number of observations.
5. In general, what is the difference between sample average and population mean? (2)
Population average requires taking the mean of a population while sample average takes the
average of a sample.
6. Based on your data, provide an unbiased estimate of the population mean? (1)
=106.9465
7. Given that your sample is only 37 out of a population of over 80,000, is your sample average
likely to be the same as the population mean? (1)
It is not likely that the sample and population mean are the same.
8. Does this indicate that your sample and sample average are biased? Please explain. (5)
The population and sample mean being different does not mean that
there is bias. Bias can occur from the way the sample was collected. A
sample can be collected in a way that overrepresents or
underrepresents certain segment of the population.
9. What is the sample standard deviation? Show the formula. (2)
Sample SD= 5.465
= variance
=Sample Standard deviation
10. If a large number of random samples of size 37 are taken from the population, and the sample
average were calculated for each sample, calculate an estimate of the standard deviation of the
distribution of sample averages (again, only use your data, not the rest of the dataset). Show
your formula. (2)
To estimate the standard deviation of the distribution of sample averages:
s/sqrt of n
Calculating the result:
17.498747
So, the estimated standard deviation of the distribution of sample averages is approximately
17.498747
11. What will be the distribution of these sample averages? Please explain. (5)
There will be a normal distribution. The Central Limit Theorem states that as the sample size
increases, the distribution of the sample mean approaches a normal distribution.
12. What is a 95% confidence interval of the population mean? Show work. (5)
X bar +- z (s/sqrt of n)
106.9465 +- 1.96(5.465/sqrt of 37)
106.9465 ± 1.778
Lower 105.168
Upper 108.725
We are 95% confident that pop mean lies between 105.168 and 108.725.
13. Test the hypothesis that the population mean is _______ at the 5% significance level. Show all
steps. (5) Test the mean 106 at the 5% significance level
Null Hypothesis (H0): The population mean is 106
H0: μ) is equal to 106.
(Ha): The population mean (μ) is not equal to 106.
Step 2: Calculate the Test Statistic
T= (sample mean – pop mean)/sample SD/sqrt of sample size
T =1.257
Df=37-1=36
3. Calculate the p-value
= .216848
Test:
.216848>.05
Therefore, we accept the null hypothesis