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# Statistics: 1. When rolling a die, is this an example

### Resolved Question:

Statistics:
1. When rolling a die, is this an example of a discrete or continuous random variable? Explain your reasoning.
2.Calculate the mean and standard deviation of the probability distribution created by rolling a die. Either show work or explain how your answer was calculated.
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)?
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)?
5.Give the standard deviation for the mean and median column. Compare these and be sure to identify which has the least variability?
6.Based on questions 3, 4, and 5 is the mean or median a better estimate for the parameter of interest? Explain your reasoning.
7.Give and interpret the 95% confidence interval for the hours of sleep a student gets
8.Give and interpret the 99% confidence interval for the hours of sleep a student gets.
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.
Submitted: 2 years ago.
Category: Calculus and Above
Expert:  Scott replied 2 years ago.

Hi there,

Please post all the data for this problem.

Thanks,

Scott

Customer: replied 2 years ago.

Statistical Concepts:

• Data Simulation

• Discrete Probability Distribution

• Confidence Intervals

Calculations for a set of variables

Ø Open the class survey
results that were entered into the MINITAB worksheet.

Ø We want to calculate the
mean for the 10 rolls of the die for each student in the class. Label the
column next to die10 in the Worksheet with the word mean
. 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.

Ø 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.

Calculating Descriptive Statistics

Ø 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.

Calculating Confidence Intervals for one
Variable

Ø Open the class survey
results that were entered into the MINITAB worksheet.

Ø 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.

Ø We are also interested in
the same analysis with a 99% confidence interval. Use the same steps except
select the Options button and change
the Confidence level: to 99.

Expert:  Scott replied 2 years ago.

Hi there,

Please do post the data itself when you have a chance, since it is required to solve this question. You can use a free sharing site like http://www.mediafire.com to upload it and then post the sharing link here.

Thanks again,

Scott

Customer: replied 2 years ago.
I already sent all the information and how to doit on minitab. I do not have a minitab that is why I cannot do it but all the information you need is already there. Thank you.
Expert:  Scott replied 2 years ago.

You did send the instructions, but that's not what I need. You haven't sent the data itself, yet. I need the worksheet with all the data.

Thanks,

Scott

Customer: replied 2 years ago.
 Race Car TV Money Coin Die1 Die2 Die3 Die4 Die5 Die6 Die7 Die8 Die9 Die10 W blue 3 4.50 7 2 5 4 3 1 4 4 2 5 2 B white 4 2.65 4 3 6 6 4 6 3 6 3 2 6 B silver 5 12.50 5 4 4 5 5 5 5 1 1 4 3 W black 3 42.60 6 3 3 3 6 2 6 2 5 3 4 H green 2 5.20 3 2 4 4 1 4 3 4 6 1 2 W silver 6 6.80 4 2 5 5 4 3 2 5 3 6 1 H blue 5 21.20 5 3 3 2 2 4 1 4 4 5 3 B dark blue 4 30.88 4 5 2 3 5 5 3 3 5 3 2 W orange 3 6.54 3 6 1 4 4 2 5 6 2 4 4 H blue 2 1.23 4 5 1 1 5 1 1 2 3 2 5 W silver 3 52.74 5 4 3 3 6 6 4 5 4 4 4 B black 1 28.56 4 3 4 5 6 5 2 1 5 1 3 W green 4 14.68 3 4 3 4 2 3 6 4 1 5 1 W silver 3 4.61 7 5 5 3 4 4 1 5 6 6 2 H blue 2 47.30 2 3 6 6 5 2 2 6 5 2 5 B red 3 19.56 4 2 4 3 2 1 5 2 3 1 6 H blue 5 22.78 5 1 2 4 1 6 4 5 4 4 4 B silver 4 33.84 4 3 5 2 5 5 3 4 2 2 6 W red 3 6.93 6 4 3 4 2 6 2 3 5 3 3 H black 2 7.00 7 5 4 5 1 4 4 5 1 2 2
Expert:  Scott replied 2 years ago.

Thanks, ***** ***** upload the full excel file, since the "hours of sleep a student" information is still missing.

You can use a free sharing site like http://www.mediafire.com/ to upload it and then post the sharing link here.

Thanks,

Scott

Customer: replied 2 years ago.

Im sorry, this is all I got please let me know if it helps.

Thoughts and insights to the week 6 lab

You can complete these calculations in Excel as well. When you open the data in the Excel format,
type "mean" in the column after "die10".
Then in cell X2 type =AVERAGE(N2:W2) to calculate the mean for that roll
of the die. Then use this same formula
to determine the average for all the remaining rows. In the next column to the right of that, type
"median" after the "mean". Then in cell
y2 type =MEDIAN(N2:W2) and use that same formula in the rows of that column.

Then under each of those columns (in my sheet this is in
cells X22 and Y22, type in =AVERAGE(X2:X21) and the same for the Y column. Under those cells, type in =STDEV(X2:X21) and
the same for the Y column so that you have the mean and standard deviation for
the mean and of the median.

We then need to find the confidence interval for the SLEEP
variable. Under that column, in cell
G22, type =AVERAGE(G2:G21). Under that
in cell G23, type =STDEV(G2:G21). Now
we can find the maximum error of the confidence interval. In cell G24, type
=CONFIDENCE.T(0.05,G23,20). The 0.05 is
1 minus the confidence interval, the C23 is the standard deviation, and 20 is
the number in our sample. You then need
to calculate the confidence interval from this
maximum error by subtracting it from the mean and adding it to the mean
as shown on page 320 of the text.

Finally, you can go one more cell down to G25 and type
=CONFIDENCE.T(0.01,G23,20) to find the maximum error for a 99% confidence
interval. Again, you would need to subtract
this and add it to find the actual confidence interval.

Question 1: list all the possible values when you roll a die

Question 2: this is calculated by hand using the formulas on
pages 194 and 195 of the text

Question 3: this is from Minitab or Excel and is based on
the mean of the means

Question 4: this is from Minitab or Excel and is based on
the mean of the medians

Question 5: from Minitab or Excel

Question 6: You can look to page 68 in the text for some
guidance on answering this question

Questions 7 and 8: from Minitab or Excel

Question 9: based on your understanding of confidence
intervals

Customer: replied 2 years ago.

Im sorry, this is all I got please let me know if it helps.

Thoughts and insights to the week 6 lab

You can complete these calculations in Excel as well. When you open the data in the Excel format,
type "mean" in the column after "die10".
Then in cell X2 type =AVERAGE(N2:W2) to calculate the mean for that roll
of the die. Then use this same formula
to determine the average for all the remaining rows. In the next column to the right of that, type
"median" after the "mean". Then in cell
y2 type =MEDIAN(N2:W2) and use that same formula in the rows of that column.

Then under each of those columns (in my sheet this is in
cells X22 and Y22, type in =AVERAGE(X2:X21) and the same for the Y column. Under those cells, type in =STDEV(X2:X21) and
the same for the Y column so that you have the mean and standard deviation for
the mean and of the median.

We then need to find the confidence interval for the SLEEP
variable. Under that column, in cell
G22, type =AVERAGE(G2:G21). Under that
in cell G23, type =STDEV(G2:G21). Now
we can find the maximum error of the confidence interval. In cell G24, type
=CONFIDENCE.T(0.05,G23,20). The 0.05 is
1 minus the confidence interval, the C23 is the standard deviation, and 20 is
the number in our sample. You then need
to calculate the confidence interval from this
maximum error by subtracting it from the mean and adding it to the mean
as shown on page 320 of the text.

Finally, you can go one more cell down to G25 and type
=CONFIDENCE.T(0.01,G23,20) to find the maximum error for a 99% confidence
interval. Again, you would need to subtract
this and add it to find the actual confidence interval.

Question 1: list all the possible values when you roll a die

Question 2: this is calculated by hand using the formulas on
pages 194 and 195 of the text

Question 3: this is from Minitab or Excel and is based on
the mean of the means

Question 4: this is from Minitab or Excel and is based on
the mean of the medians

Question 5: from Minitab or Excel

Question 6: You can look to page 68 in the text for some
guidance on answering this question

Questions 7 and 8: from Minitab or Excel

Question 9: based on your understanding of confidence
intervals

Customer: replied 2 years ago.

 Drive State Temp Rank Height Shoe Sleep Gender Race Car TV Money Coin Die1 Die2 Die3 Die4 Die5 Die6 Die7 Die8 Die9 Die10 36 MI 51 8 61 10 7 M W blue 3 4.50 7 2 5 4 3 1 4 4 2 5 2 80 NV 52 7 69 12 8 M B white 4 2.65 4 3 6 6 4 6 3 6 3 2 6 76 PA 50 9 71 11 4 M B silver 5 12.50 5 4 4 5 5 5 5 1 1 4 3 88 CA 53 5 63 6 5 F W black 3 42.60 6 3 3 3 6 2 6 2 5 3 4 54 FL 51 4 70 9 8 F H green 2 5.20 3 2 4 4 1 4 3 4 6 1 2 6 OR 51 2 74 13 10 M W silver 6 6.80 4 2 5 5 4 3 2 5 3 6 1 4 NY 52 7 69 9 7 F H blue 5 21.20 5 3 3 2 2 4 1 4 4 5 3 55 OH 54 6 67 9 8 F B dark blue 4 30.88 4 5 2 3 5 5 3 3 5 3 2 36 TX 55 8 66 7 5 M W orange 3 6.54 3 6 1 4 4 2 5 6 2 4 4 71 MI 53 9 64 8 6 F H blue 2 1.23 4 5 1 1 5 1 1 2 3 2 5 25 GA 52 3 69 9 7 M W silver 3 52.74 5 4 3 3 6 6 4 5 4 4 4 28 NY 51 4 67 7 4 F B black 1 28.56 4 3 4 5 6 5 2 1 5 1 3 73 FL 58 6 70 12 7 F W green 4 14.68 3 4 3 4 2 3 6 4 1 5 1 63 PA 57 5 66 10 8 F W silver 3 4.61 7 5 5 3 4 4 1 5 6 6 2 78 CA 52 1 71 9 9 M H blue 2 47.30 2 3 6 6 5 2 2 6 5 2 5 94 KY 57 2 74 11 8 M B red 3 19.56 4 2 4 3 2 1 5 2 3 1 6 36 OR 54 5 73 9 7 M H blue 5 22.78 5 1 2 4 1 6 4 5 4 4 4 25 CA 58 7 69 8 6 F B silver 4 33.84 4 3 5 2 5 5 3 4 2 2 6 76 NY 52 8 65 9 7 F W red 3 6.93 6 4 3 4 2 6 2 3 5 3 3 80 CA 54 9 70 10 8 F H black 2 7.00 7 5 4 5 1 4 4 5 1 2 2
Customer: replied 2 years ago.

Im sorry I do not know how to se the site.

Expert:  Scott replied 2 years ago.

Hi there,

Please visit a free sharing site like http://www.sendspace.com or http://www.wikisend.com and choose the excel file to upload. Once it's uploaded, paste the sharing/download link here in a reply to me.

Thanks,

Scott

Customer: replied 2 years ago.
http://www.sendspace.com/file/dfrhgh
Expert:  Scott replied 2 years ago.

Excellent, that's perfect. Give me about 30 minutes to solve all the questions.

Thanks,

Scott

Expert:  Scott replied 2 years ago.

Here you go:

Let me know if you have any questions,

Scott

Satisfied Customers: 17710
Experience: Over 13,000 accepts & 100% feedback in the old math category
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