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 probabilityThere 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 = 0.3202StDev of medians = 0.472The 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%)

Math 221 Week 6 Live LectureNote: This should be 99.0


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!

Note: This should be 99.0 (Typo)


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!

http://www.facebook.com/statcave

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Math 221 week 6 live lecture