Math 221 week 6 live lecture

Math 221 Week 6 Live Lecture

B Heard
(Don’t copy or post without my
permission, students may download a
copy for personal use)

• The following are examples of the Week 6 Lab,
please note that I CHANGED the data!

1. When rolling a die, is this an example of a
discrete or continuous random variable?
Explain your reasoning.

– You should be able to answer this
• Read about discrete and continuous variables

2. Calculate the mean and standard deviation of
the probability distribution created by rolling
a four sided die. Either show work or explain
how your answer was calculated.

– For the sake of example, I am going to use a four-
sided die (your lab deals with a six-sided die)

• In other words, my die would look like a
pyramid. You could roll a 1,2,3 or 4 and they
are all equally likely.

• To get the mean

Mean = ƩxP(x) = 1(1/4)+2(1/4)+3(1/4)+4(1/4) =
10/4 or 2.5

Die Value times the probability
There are four equally likely sides, so the
probability for each would be ¼.

• To get the standard deviation

St. Dev. = sqrt((1-2.5)2(1/4)+ (2-2.5)2(1/4)+ (3-
2.5)2(1/4)+ (4-2.5)2(1/4) = sqrt(1.250) = 1.118

REMEMBER WE WERE DEALING WITH A FOUR
SIDED DIE

3. Give the mean for the mean column of the
Worksheet. Is this estimate centered about
the parameter of interest (the parameter of
interest is the answer for the mean in
question 2)?

I CHANGED THE DATA

• Type the word “Mean” to the right of Die10

• Pull up Calc > Row Statistics and select the
radio-button corresponding to Mean. For
Input variables: enter all 10 rows of the die
data. Go to the Store result in: and select the
Mean column. Click OK and the mean for each
observation will show up in the Worksheet.

• Now I have the means calculated in the
“Mean” column

• We also want to calculate the median for the
10 rolls of the die. Label the next column in
the Worksheet with the word Median. Repeat
the above steps but select the radio-button
that corresponds to Median and in the Store
results in: text area, place the median
column.

• Same process as Mean, except choose Median
radial button and change Store result to
Median by double clicking on Median in your
list on the left.

• Calculate descriptive statistics for the mean
and median columns that where created
above. Pull up Stat > Basic Statistics > Display
Descriptive Statistics and set Variables: to
mean and median. The output will show up in
your Session Window. Print this information.

So number 3 wants the “Mean of Means”
(From previous chart)
Mean of means = 2.64 yes, this is generally
centered around the parameter of interest
(the 2.5 I calculated in number 2)
Honestly I would have liked for it to be a tad
closer (but remember I changed data at a
whim and probably put too many 3’s and 4’s
in rather than actually rolling a 4-sided die)

4. Give the mean for the median column of the
Worksheet. Is this estimate centered about the
parameter of interest (the parameter of interest
is the answer for the mean in question 2)?

Mean of medians = 2.775, this is definitely farther
away from the parameter of interest (the 2.5 I
calculated mathematically in number 2)

5. Give the standard deviation for the mean and
median column. Compare these and be sure to
identify which has the least variability?

StDev of means = 0.3202
StDev of medians = 0.472
The standard deviation of the means is smaller,
thus it has less variability than the medians.
This would mean the data for the means is
grouped closer together.

6. Based on questions 3, 4, and 5 is the mean or
median a better estimate for the parameter of
interest? Explain your reasoning.

In my case, the mean seems to be a better
estimate because it is closer to the
mathematically calculated mean and the
standard deviation is less than that of the
medians meaning the means are grouped closer
together.

7. Give and interpret the 95% confidence
interval for the hours of sleep a student gets.

I changed the data! So these are not the
answers to your lab!

• We are interested in calculating a 95%
confidence interval for the hours of sleep a
student gets. Pull up Stat > Basic Statistics > 1-
Sample t and set Samples in columns: to
Sleep. Click the OK button and the results will
appear in your Session Window.


Therefore, the 95% confidence interval would be (6.232, 8.168). I would be
95% confident that the true mean number of hours a student sleeps would be
between those two values.

I changed the data! So these are not the answers to your lab!

8. Give and interpret the 99% confidence
interval for the hours of sleep a student gets.

(Same approach as number 7, but MAKE SURE
you click options and change confidence to
99%)

Note: This should
be 99.0

Note: This should
be 99.0 (Typo)

Therefore, the 99% confidence interval would be (5.405, 8.995). I would be
99% confident that the true mean number of hours a students sleeps would be
between those two values.

I changed the data! So these are not the answers to your lab!

9. 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.

The 99% confidence interval is wider than the
95%, which is always the case. To get more
confidence, the bounds widened (i.e. it’s the
only way you can get more certainty).

• I will post a link to these charts in the
“Statcave” at www.facebook.com/statcave

• See you Sunday!

Math 221 week 6 live lecture

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Math 221 week 6 live lecture