# 131

The first section of this final examination assess whether you can make basic statistical computations. For the purposes of this section any set of numbers will do. The following is the number of times ⚥ played a particular song in concerts over the course of his lifetime. The number of times a song was played is based on actual performance set lists. Use the data in the second column, the number of times a song was played, for this first section of the final.

SongSetList count
Purple Rain 1005
Kiss 758
Let's Go Crazy 701
1999 638
Little Red Corvette 632
Take Me With U 608
When Doves Cry 540
Raspberry Beret 537
Controversy 536
Baby I'm a Star 488
Nothing Compares 2 U 423
Do Me, Baby 421
U Got the Look 410
Delirious 368
The Beautiful Ones 368
I Would Die 4 U 355
1. What is the highest level of measurement that this data could be considered to be?
2. Calculate the sample size n:
3. Calculate the minimum:
4. Calculate the first quartile Q1:
5. Calculate the median:
6. Calculate the third quartile Q3:
7. Calculate the maximum:
8. Which of the following is the correct box and whisker plot with outliers for this data? Note that the two images are of the same data, they were produced with two different tools.
9. Calculate the range:
10. If the data is divided into five classes, calculate the width of a single class:
11. Calculate the class upper limits and the frequencies for the data using five classes. Use these results to choose the correct frequency histogram.
12. What is the shape of the histogram?
13. Calculate the mode:
14. Calculate the mean. Keep two decimal places:
15. Calculate the sample standard deviation sx. Keep two decimal places:
16. Calculate the standard error SE of the sample mean. Keep two decimal places:
17. Calculate t-critical for a 95% confidence level. Keep two decimal places:
18. Calculate the margin of error E of the sample mean. Keep two decimal places:
19. Calculate the lower bound for the 95% confidence interval for the population mean μ. Round to a whole number:
20. Calculate the upper bound for the 95% confidence interval for the population mean μ. Round to a whole number:
21. The data for the band setlist below has a mean of 238.6875. Use the above 95% confidence interval to test whether the population mean for ⚥ could be 238.6875:
H0: µ = 238.6875
H1: µ ≠ 238.6875

Do you reject or fail to reject the null hypothesis at an alpha of 5%? Note that the connection between the artists is ⚥ playing the second song in the following setlist.
SongSetlist count
Dazed and Confused 438
Whole Lotta Love 314
Moby Dick 312
Since I've Been Loving You 299
Stairway to Heaven 271
Communication Breakdown 266
Heartbreaker 255
Black Dog 229
White Summer/Black Mountain Side 221
Rock and Roll 211
How Many More Times 199
I Can't Quit You Baby 185
The Song Remains the Same 173
Train Kept A-Rollin' 154
You Shook Me 147
Over the Hills and Far Away 145
22. The stairs and platforms below are known as the Haiku stairs or "The Stairway to Heaven" in some circles. The stairs climb Pu'u Keahi a Kahoe on Oahu. In keeping with the non-serious nature of the data in this final, the following is a linear regression exercise based on data from thte steepest section of the stairs seen above.

Mile marker Height (feet)
3.5 1000
3.7 1900
4.1 2000
4.5 2800

For the paired data, calculate the sample size n:
23. Calculate the slope. Round to a whole number:
24. Calculate the y-intercept. Round to a whole number, retain the negative sign if any:
25. Calculate the correlation coefficient r for the data. If the correlation is negative, include the negative sign, rounding your answer to two decimal places.
26. Is the correlation none, weak/low, moderate, strong/high, or perfect?
27. Use the slope and intercept to predict the height at the 3.9 mile marker. Round your result to a whole number:
28. A family in Madolehnihmw has a child in the eighth grade who enjoys to write and is a good writer. The parents want to send their child to a high school that potentially produces good writers. The only data the parents have to work with are the essay scores on the spring 2016 COMET entrance examination. The parents have narrowed their choice down to choosing between Our Lady of Mercy Catholic High School and Madolenihmw High School. Use the data to help advise the parents in making their choice.
• Which high school produced the higher COMET essay scores (total possible 50)? Based on what?
• Is the difference significant? Why?
• Based only on the COMET essay score data, which school, if either, should the child be sent to? Why?
OLMCHS MHS A
33 39
36 28
35 34
38 35
28 42
36 40
49 34
49 47
33 42
44 35
47 48
33 40
36 37
33 42
48 39
29 41
48 40
37 30
37 42
43 45
35
35
36

Do not simply write down any and all statistics you have ever learned. Cite specific statistics or charts that support that answer. When citing a statistic or statistics, include both the name of the statistic, the numeric value, and why that statistic is meaningful.