MS 150 Statistics spring 2007 Mx • Name:

Using World Health Organization data, Forbes magazine ranked 194 countries from fattest to thinest. The Federated States of Micronesia was number two on the list - the second "fattest" country on the planet Earth behind only Nauru. While there are some issues with the methodology and skeletal muscle impacts on BMI for Pacific Islanders, the nation is facing an epidemic of non-communicable diseases due to life style choices including those resulting from excess body fat. Excess body fat is the intake of more calories per day than one burns per day. The right number of calories to maintain you weight varies as a result of many factors. On average, the recommended daily intake of calories is 1940 for women and 2550 for men. One of the contributors to excess body fat is "fast food." "Fast food" is "fat food." One single double cheeseburger with bacon can be half of your recommended daily calorie intake. Add in the french fries and the soda, and that one meal could take you over your daily recommended calorie intake. Anything else you eat that day will simply become fat in your body. This statistics midterm looks at the calorie content of fast food hamburgers and cheeseburgers from some of the fast food chains in the United States.¹

Part I: Basic statistics, frequencies, histogram, z-scores, normal distribution.

The following section is based on the calorie data in the table.

1. __________ What level of measurement is the data?
2. __________ Find the sample size n for the data.
3. __________ Find the minimum.
4. __________ Find the maximum.
5. __________ Find the range.
6. __________ Find the median.
7. __________ Find the mode.
8. __________ Find the sample mean x.
9. __________ Find the sample standard deviation sx.
10. __________ Find the sample coefficient of variation CV.
11. __________ If this data were to be divided into five bins, what would be the width of a single bin?
12. Determine the frequency and calculate the relative frequency using five bins. Record your results in the table provided.

    Frequency table

    Bins (x)	Frequency (f)	Rel. Freq. p(x)
    _______	_______	_______
    _______	_______	_______
    _______	_______	_______
    _______	_______	_______
    _______	_______	_______
    Sum:	_______	_______

13. Sketch a relative frequency histogram chart of the data here or on the back, labeling your horizontal axis and vertical axis as appropriate.
14. ____________________ What is the shape of the distribution?
15. ____________________ Use the mean µ and standard deviation σ calculated above to find the z-score for the Wendy's Triple Cheeseburger.
16. ____________________ Is the number of calories in a Wendy's Triple Cheeseburger ordinary or extraordinary?
17. __________ In the Federated States of Micronesia, men and women between the age of 20 and 85 years old have a mean Body Mass Index (BMI) of µ = 31.0 and a standard deviation of σ = 5.7 according to data provided by the FSM to the World Health Organization (WHO). For Micronesians a BMI of 27 or higher is overweight. What percent of the Micronesians are at a BMI of 27 or higher? In other words, what percentage of the population is overweight?
18. __________ Forbes magazine, using WHO data and a BMI of 25³, determined that in the FSM 91.1% of the people are overweight. Does your calculation support this conclusion?

Part III: Linear regression

28 February 2007: As this paragraph is being written, the Polynesian Voyaging Society canoes Hokule'a and Maisu are less than 240 kilometers to the east-northeast of Pohnpei. The canoes have sailed from Hawaii. The two canoes left Catalin Channel in the Majuro lagoon ten days ago headed for Pohnpei. The canoes are being navigated using the traditional navigation systems of Satawal as taught by Mau Pialug. The voyage is being called Ku Holo Mau in honor of Mau. The Maisu is a gift of the people of Hawaii to the people of Satawal, Mau's home island, and will remain in Yap. The distance covered by the two canoes varies with wind, current, and weather conditions. The following data is the distance in km from Majuro for the two canoes at three in the afternoon each day Pohnpei time. In other words, the distances are the kilometers covered in a 24 hour time period.

19. __________ Calculate the slope of the linear trend line for the data.
20. __________ Calculate the y-intercept for the data.
21. __________ Is the correlation positive, negative, or neutral?
22. __________ Determine the correlation coefficient r. Keep at least four significant (non-zero) digits. Use Format: Cells: Numbers to increase the number of decimal places displayed.
23. __________ Is the correlation none, low, moderate, high, or perfect?
24. __________ Does the relationship appear to be linear or non-linear?
25. __________ Determine the coefficient of determination.
26. __________ What percent in the variation in the days accounts for the variation in the distance?
27. __________ Pohnpei is 283 kilometers from Majuro. Using the equation above, calculate the day to two decimal places on which the canoes are expected to arrive. [Remember, this question was written on Wednesday night prior to arrival of the canoes!]
28. __________ When did the canoes arrive?

Table of statistical functions used by OpenOffice

Statistic or Parameter	Symbol	Equations	OpenOffice
Square root			=SQRT(number)
Sample mean	x	Σx/n	=AVERAGE(data)
Sample standard deviation	sx		=STDEV(data)
Sample Coefficient of Variation	CV	sx/x	=STDEV(data)/AVERAGE(data)
Calculate a z value from an x	z	=	=STANDARDIZE(x;μ;σ)
Find a probability p (the area to the left of x) from an x value			=NORMDIST(x;μ;σ;1)
Find an x value from a probability p (the area to the left of p)			=NORMSINV(p;μ;σ)
Slope	b		=SLOPE(y data;x data)
Intercept	a		=INTERCEPT(y data;x data)
Correlation	r		=CORREL(y data;x data)
Coefficient of Determination	r²		=(CORREL(y data;x data))^2

¹While Micronesians may be "wired to eat", they are not wired to be obese.

²Not all calories are equal. Data for the table from FastFood.com and the Rodale Institute.

³Internationally 25 is used. The appropriate BMI threshold for being overweight varies by the way in which skeletal muscle is distributed, along with deep visceral fat, and bone size. China uses a BMI of 23, the United States 25, and Pacific Islanders should use 27.