MATH 221 Statistics for Decision
Making Week 6 iLab
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Short Answer Writing Assignment
All answers should be complete
sentences.
We need to find the confidence
interval for the SLEEP variable. To do this, we need to find the mean and
then find the maximum error. Then we can use a calculator to find the
interval, (x – E, x + E).
First, find the mean. Under
that column, in cell E37, type =AVERAGE(E2:E36). Under that in
cell E38, type =STDEV(E2:E36). Now we can find the maximum
error of the confidence interval. To find the maximum error, we use the
“confidence” formula. In cell E39, type =CONFIDENCE.NORM(0.05,E38,35).
The 0.05 is based on the confidence level of 95%, the E38 is the standard
deviation, and 35 is the number in our sample. You then need to calculate
the confidence interval by using a calculator to subtract the maximum error
from the mean (x-E) and add it to the mean (x+E).
- Give and interpret the 95% confidence interval for the
hours of sleep a student gets. (6 points)
Then, you can go down to cell E40
and type =CONFIDENCE.NORM(0.01,E38,35) to find the maximum error for a
99% confidence interval. Again, you would need to use a calculator to
subtract this and add this to the mean to find the actual confidence interval.
- Give and interpret the 99% confidence interval for the
hours of sleep a student gets. (6 points)
- Compare the 95% and 99% confidence intervals for the
hours of sleep a student gets. Explain the difference between these
intervals and why this difference occurs. (6 points)
In the week 2 lab, you found the
mean and the standard deviation for the HEIGHT variable for both males and
females. Use those values for follow these directions to calculate the
numbers again.
(From week 2 lab: Calculate
descriptive statistics for the variable Height by Gender. Click on Insert
and then Pivot Table. Click in the top box and select all the data
(including labels) from Height through Gender. Also click
on “new worksheet” and then OK. On the right of the new sheet,
click on Height and Gender, making sure that Gender is in
the Rows box and Height is in the Values box.
Click on the down arrow next to Height in the Values box and
select Value Field Settings. In the pop up box, click Average then
OK. Write these down. Then click on the down arrow next to Height
in the Values box again and select Value Field Settings. In
the pop up box, click on StdDev then OK. Write these values
down.)
You will also need the number of
males and the number of females in the dataset. You can either use the
same pivot table created above by selecting Count in the Value Field
Settings, or you can actually count in the dataset.
Then in Excel (somewhere on the data
file or in a blank worksheet), calculate the maximum error for the females and
the maximum error for the males. To find the maximum error for the
females, type =CONFIDENCE.T(0.05,stdev,#), using the females’ height
standard deviation for “stdev” in the formula and the number of females in your
sample for the “#”. Then you can use a calculator to add and subtract
this maximum error from the average female height for the 95% confidence
interval. Do this again with 0.01 as the alpha in the beginning of the
formula to find the 99% confidence interval.
Find these same two intervals for
the male data by using the same formula, but using the males’ standard
deviation for “stdev” and the number of males in your sample for the “#”.
- Give and interpret the 95% confidence intervals for
males and females on the HEIGHT variable. Which is wider and
why? (9 points)
- Give and interpret the 99% confidence intervals for
males and females on the HEIGHT variable. Which is wider and
why? (9 points)
- Find the mean and standard deviation of the DRIVE
variable by using =AVERAGE(A2:A36) and =STDEV(A2:A36).
Assuming that this variable is normally distributed, what percentage of
data would you predict would be less than 40 miles? This would be
based on the calculated probability. Use the formula =NORM.DIST(40,
mean, stdev,TRUE). Now determine the percentage of data points
in the dataset that fall within this range. To find the actual
percentage in the dataset, sort the DRIVE variable and count how many of
the data points are less than 40 out of the total 35 data points.
That is the actual percentage. How does this compare with your prediction?
(12 points)
|
Mean
______________
Standard deviation ____________________
Predicted percentage
______________________________
Actual percentage
_____________________________
Comparison ___________________________________________________
______________________________________________________________
|
- What percentage of data would you predict would be
between 40 and 70 and what percentage would you predict would be more than
70 miles? Subtract the probabilities found through =NORM.DIST(70, mean,
stdev, TRUE) and =NORM.DIST(40, mean, stdev, TRUE) for the
“between” probability. To get the probability of over 70, use the
same =NORM.DIST(70, mean, stdev, TRUE) and then subtract the result
from 1 to get “more than”. Now determine the percentage of data
points in the dataset that fall within this range, using same strategy as
above for counting data points in the data set. How do each of these
compare with your prediction and why is there a difference?
(12 points)
|
Predicted percentage between 40
and 70 ______________________________
Actual percentage
_____________________________________________
Predicted percentage more than 70
miles ________________________________
Actual percentage
___________________________________________
Comparison
____________________________________________________
_______________________________________________________________
Why?
__________________________________________________________
_______________________
|
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