MS 150 Statistics Final Examination • Name:

Over the past decade Xavier High School student essays written for the COMET entrance test have taken first rank among the high schools in the FSM. This year the Xavier essays lost their first rank position and another school has taken first rank based on median score. The new top of the essay rank order is Our Lady of Mercy Catholic High School in Pohnpei. The data consists of the essay scores for 22 students at Our Lady of Mercy Catholic High School. The essay is scored out of 50 points.

1. __________ Calculate the sample size n.
2. __________ Calculate the minimum (quartile 0).
3. __________ Calculate the first quartile (Q1).
4. __________ Calculate the median (quartile 2).
5. __________ Calculate the third quartile (Q3).
6. __________ Calculate the maximum (quartile 4).
7. __________ Calculate the Inter-Quartile Range (IQR).
8. Sketch the box plot for the data.
9. __________ Calculate the range.
10. __________ If the data is divided into three classes,
    what is the width of a single class?
11. Determine the frequency and calculate the relative
    frequency for the data using three classes.
    Record your results in the table provided.
    

    Class upper limits	Frequency F	Rel. Freq.
    Sums:

12. __________ What is the shape of the histogram?
13. __________ Calculate the mode.
14. __________ Calculate the mean.
15. __________ Calculate the sample standard deviation sx.
16. __________ Calculate the standard error SE of the sample mean.
17. __________ Calculate the degrees of freedom.
18. __________ Calculate t-critical for a 95% confidence level.
19. __________ Calculate the margin of error E of the sample mean.
20. Calculate the 95% confidence interval for the population mean μ
    p(__________ < μ < __________) = 0.95
21. __________ Based on the OLMCHS data, what is the probability that an OLMCHS student will score greater than 42 on the essay?


The following data is measurements of the apparent depth of an object under layers of glass versus the actual depth of the object under the layers of glass. Due to refraction, objects under glass appear slightly closer than they actually are. The slope of the apparent depth versus actual depth line is the index of refraction of glass.



Apparent depth (cm)	Actual depth (cm)
0.0	0.0
0.5	1.0
1.0	1.9
1.5	2.4
2.0	3.1


Data courtesy of Rowena Mauricio

22. _________ For the paired data, calculate the sample size n (the number of data pairs).
23. ______________ Calculate the slope of the linear regression for the data.
24. ______________ Calculate the y-intercept of the linear regression for the data.
25. ______________ Is the relation positive, negative, or neutral?
26. ______________ Calculate the correlation coefficient r for the data.
27. ______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
28. ______________ Determine the coefficient of determination.
29. ______________ Use the slope and intercept to predict the actual depth of an object that has an apparent depth of 1.75 cm under the glass.
30. ______________ Use the slope and intercept to predict the apparent depth of an object that an actual depth of 1.5 cm under the glass.

Data exploration: Round Island Relay Race

On 30 March 25 runners from election district three ran the round island relay race. Each runner ran two miles. This open data exploration is based on the estimated duration of time in minutes for each runner. Time-stamped photographs taken that day provided rough estimates for each runner's time. This data set represents an exercise in data exploration from the field of exercise sport science.

Imagine that you are the team statistician. Your job is to provide statistical information in a report of use to the coach. There are plans to run this race again with teams invited from abroad. Based on the time data, what useful statistics can you report? The coach wants to be able to make decisions on who should start, who should anchor, who should be retained, and who should be replaced and why. Provide a complete statistical report on the data. For any decisions, cite statistical support. Look also for unusual data, if any, reporting the unusual data and why that data is unusual. Provide statistical values that support your recommendations.

* State senator Robert Nakasone was slated to run anchor and did run anchor. Due to a close finish, however, another runner also ran the final two miles carrying the District 3 sash across the finish line for the win. Other members of the team joined in for the final two miles, following the lead District 3 runner. The team also included Marson Etnol, Mihter Wendolin, Anderson Ponapart, Amanda Wendolin, and Pauraheko Ardos. Images and notes from the run are available in a Wordpress blog article on the round-Pohnpei relay run.