1. The probability of passing a Statistics 203 final exam is 0.80. Which of the following statements gives a valid interpretation of this probability?
a. Out of every 10 students, 8 will pass the final exam.
b. In the long run, the proportion of students passing the final exam is 0.80.
c. For any group of 10 students, at least 8 students will pass the final exam.
d. In the long run, the proportion of students passing the final exam is 0.50.
2. Suppose you have a large random sample from a population. Furthermore, suppose that the population distribution of measurements does not follow a normal istribution. What does the central limit theorem tell us?
a. For large samples, the distribution of the data is approximately normal.
b. For large samples, the distribution of the population mean, μ, is approximately normal.
c. For large samples, the distribution of the sample mean, € X , is approximately normal.
d. For large samples, the sample mean, € X , is very close to
3. Hypothesis: Individuals who listen to music whilst studying for exams will achieve significantly higher exam grades than will individuals who study in silence. A research study is conducted to see if there is evidence in favour of the hypothesis. Thinking about this research hypothesis, which of the below would be an appropriate summary of a statistical significant difference in this setting?
a. The observed average exam grades for students who listen to music are about the same as the average exam grades for students who study in silence.
b. The observed difference in average exam grade for students who listen to music from the average exam grade for students who study in silence can be attributed to chance.
c. The observed average exam grade for students who listen to music is larger than the average exam grade for students who study in silence.
d. The observed difference between the average exam grade for students who listen to music and the average exam grade for students who study in silence is so large as to be unlikely to have occurred by chance.
4. According to the US Census Bureau, the average number of children per American family is 2.2. Which of the following most adequately describes this mean for the American population.
a. The mean of 2.2 children makes no sense because a family cannot have 0.2 children.
b. The mean of 2.2 is the long-term average number of children based on repeatedly sampling families from the American population.
c. The mean of 2.2 children implies that American families have 1, 2 or 3 children.
d. American families have between 2 and 3 children.
5. (10 marks) Motivated students from across Canada can participate in an annual mathematics competition. A random sample of 1,000 students is taken from each of three regions (Maritimes and Newfoundland, Central Canada and Western Canada) to compare student performance on the competition. The test was out of 60 marks.
a. Use the above plot to compare the distributions of student scores by region.
b. What is the interval covering the middle 50% of test scores observed in Western Canada (explain how you determined this interval)?
c. What percentage of students from the Western Canada scored higher than 50 marks?
d. Roughly, what is the score for the worst performing student from Central Canada in this sample of students?
e. Can you tell from this plot whether any of the distributions are uni-modal (explain)?
6. (8 marks) Metabolic rate is important in studies of dieting and exercise. The lean body mass (kg) and resting metabolic rate (cal./24hrs) for 100 men participating in a study on dieting were recorded. The histogram of the recorded resting metabolic rates is plotted below. A scatter-plot of the resting metabolic rates versus the lean body mass is also shown.
a. What percentage of men in the study had a resting metabolic rate of larger than 1350?
b. In which bin would you expect the median resting metabolic rate for this study.
c. Suppose that the correlation between resting metabolic rate and lean body mass is computed. What does correlation attempt to measure in this setting?
d. Is it appropriate to use the correlation to describe the relationship between resting metabolic rate and lean body mass (why or why not)?
7. (4 marks) An advice columnist asked divorced readers, via her advice column, whether they regretted their decision to divorce. About 30,000 responses were received, of which about 23,000 were from women. Nearly 75% of respondents said that they were glad that they divorced.
a. What type of survey is this?
b. Briefly explain why this survey is likely to be biased.
8. (2 marks) A university has 10,000 undergraduate and 5,000 graduate students. A survey of the students' opinions is conducted by first randomly selecting 100 of the 10,000 undergraduate students and then 50 of the 5,000 graduate students. Very briefly explain why this is not a simple random sample.
9. (2 marks) Average before-tax income in the City of Burnaby in 2005 for female single parent households was $46,228. This statistic was reported in the 2006 City of Burnaby Neighborhood Profile. Briefly explain why reporting the median income is likely to be a better measure of the centre for the distribution of female single parent household in 2005 than reporting the average.
10. (8 marks) The distribution of moisture content per pound of dehydrated protein concentrate is normally distributed with a mean of 3.5% and standard deviation of 0.6%.
a. Interpret the meaning of the standard deviation of 0.6% in this setting.
b. A random sample of 36 one-pound specimens is taken and the moisture content of each is measured. What is the distribution of the sample mean moisture content?
c. What is the probability that the sample mean of the 36 specimens in part b is larger than 3.8%?
d. Find the 99th percentile of the distribution of sample mean moisture content based on a sample of 36 specimens as in part b?
11. (6 marks) A simple game-of-chance at a high school fund-raising day used a single six-sided die (Note: die is the singular of dice). It costs $2 to play the game. If after rolling the die the numbers 1 or 6 are showing, the player is given a brand new $5 bill. If the numbers 2-5 are showing the player loses and has to do a silly dance.
a. What is the probability distribution for the expected monetary return of this game from the player's point of view?
b. What is the expected monetary return of this game from the player's point of view?
c. What is the minimum amount that the high school should charge to play the game if it is to expect to make a profit?
12. (3 marks) Volunteers were given a 5x5 square puzzle to solve and the time it took them to solve it was measured in seconds. The data recorded are listed below:
132, 141, 142, 143, 143, 147, 148, 149, 150, 158, 163 Find quartiles for these data.