THIS IS AN OLD COURSE SITE, FOR THE CURRENT SEMESTER, PLEASE CLICK HERE!
Block: C, Tuesday, Wednesday, Friday, 9:30–10:20 a.m.
Email: Andrew [Dot] Sanchez [at] Tufts [Dot] edu
Office Hours: Tuesday, Wednesday, 10:30–11:30 a.m., Thursday 1:20 p.m. - 2:20 p.m.
Link to the Syllabus, Updated September 13, 2015.
- Midterm 1: Wendesday, October 7, 2015, 9:30-10:20 a.m.
- Midterm 2: Friday, November 13, 2015, 9:30-10:20 a.m.
- Final: Thursday, December 17, 2015, 12:00-2:00 p.m. in BP-002
Homework 1 Due Tuesday, September 15th. Histogram of Scores.
- Section 1-2 (pg 13): 20
- Section 1-3 (pg 22): 33
- Section 2-2 (pg 51): 7, 12, 15, 20
- Section 2-3 (pg 59): 10
- Section 2-4 (pg 71): 10
- Use the frequency distributions from Exercise 15 in section 2-2 to construct two histograms
- Use the frequency distributions from Exercise 15 in section 2-2 to
construct the relative frequency polygons (similar to Example 11 in
Homework 2 Due Tuesday, September 22nd. Histogram of Scores.
Link to data collected in class: comma separated values, excel file.
- Section 3-2 (pg 93): 18, 22
- Section 3-3 (pg 109): 44
- Section 3-4 (pg 125): 16, 32
The remaining exercises are concerned with the data collected in class on Friday.
For these exercises, you may use a calculator, but should indicate how you arrived at your numerical values.
- Construct a histogram from the data collected in class (red Skittles). Does it appear to be normally distributed?
- Calculate the sample mean, median, mode, sample standard deviation, and sample variance.
- Calculate the five number summary and construct a boxplot (box-and-whisker diagram).
- Someone in class had a bag with 0 red Skittles. Someone else had a bag with 7 red Skittles. Which bag is more unusual?
- My friend did a similar experiment in her stats class but with Green M&Ms in fun sized bags. In their experiment, they had a sample mean of 2.9 Green M&Ms and a sample standard deviation of 1.55 Green M&Ms. Judging just by her data and ours, who appears to have more variation, Green M&Ms or Red Skittles?
Homework 3 Due Tuesday, September 29th. Histogram of Scores.
- Section 4-3 (pg 156): 31
- Section 4-4 (pgs 165,168): 16, 32
- Section 4-5 (pg 172): 10
- Section 4-6 (pgs 180-182): 8, 14, 16, 31
A certain disease is estimated to have a prevalence of .0048 (roughly 48 out of every 10,000 adults). A new test is devised which attempts to diagnoze those with the disease. After much testing, it is determined tohave a sensitivity of .996 and a specificity of .998.
- Construct a tree diagram which illustrates the prevalence, specificity, and sensitivity.
- Say you get a positive test, What is the probability you have the disease? Say you get a negative test, what is the probability that you do not have the disease? What does the new test appear to be good for? (Remember, correct answers must include the proper setup!)
Homework 4 Due Tuesday, October 6th. Histogram of Scores.
Note: For 5-4 #22 there is a slight change. Please write the condition as an inequality involving a finite sum and leaving n as unknown. The book asked you to then solve the inequality for n -- you DON'T have to do that!
- Section 5-2 (pgs 207-209): 8, 19
- Section 5-3 (pgs 219-220): 22, 32
- Section 5-4 (pgg 226-228 ): 15, 22*
- Section 5-5 (pgs 232-233): 4, 10
Suppose the probability of suffering a side effect from certain flu vaccine is 0.0000028 (7 cases observed in 2,500,000 trials). A plan is put in to motion to inoculate 1,000,000 people using it.
- What is the expecte number of people who will experience the side effects? Write an expression for the probability that less than 5 people experience the side effect.
- Using the mean calculated in the previous problem, write an expression that approximates the probability that less than 5 people experience the side effect. Use a calculator (or WolframAlpha) to evaluate both expressions. Is the approximation close?
Link to topics list, Updated September 29, 2015. We will discuss on Tuesday, October 6th
Link to Solutions
Histogram of Scores
Homework 5 Due Tuesday, October 20th. Histogram of Scores.
- Section 6-2 (pgs 256-258): 38, 40
- Section 6-3 (pgs 266-271): 23, 28
- Section 6-4 (pgs 280-283): 11, 13
- Section 6-5 (pgs 292-296): 16, 24
For the following problem, use the Red Skittles Data from Homework 2. For the sake of the sake of the problem, treat each bag as if it had 15 total Skittles. You may use Excel or some other program to compute your answers.
- We previously took bags of Skittles and counted how many red Skittles were in each. We wish to estimate the proportion of red Skittles in the population of all Skittles, and can treat each fun sized bag as a sample of fifteen Skittles. Calculate the sample proportions for each of the sample with the caveat that you should use the sample size of 15 and NOT the actual size of each fun sized bag. Construct a histogram of sample proportions, using a class size of 0.1. Do the sample proportions look Normally distributed?
- Estimate the population proportion of Red Skittles.
Homework 6 Due Tuesday, October 27th. Histogram of Scores.
- Section 6-6 (pg 303): 6, 8, 18
- Section 6-7 (pgs 311-314): 13, 14, 18, 24
- Section 7-2 (pgs 337-342): 19, 27
For the following problem, we again use the red Skittles data in the following form: if we pool everyone's Skittles bags together, we would have 457 Skittles with 95 of them red.
- Use the Skittles data as above to construct a 95% confidence interval for the proportion of red Skittles. Since Skittles come in five colors (red, orange, green, purple, yellow), I hypothesize that one fifth of all Skittles are red. Is this a reasonable hypothesis?
Homework 7 Due Tuesday, November 3rd. Histogram of Scores.
- Section 7-3 (pgs 355-361): 9, 16, 18
- Section 7-4 (pgs 368-371): 11, 12, 16
- Section 8-2 (pgs 396-398): 8, 29
For the following problem, we use the M&M's data from class in the following form: if we pool everyone's M&M's bags together, we would have 376 M&M's with 81 of them green.
- There are six colors of M&M's (yellow, green, blue, red, orange, and brown), so we can reasonably expect that 1/6th of all M&M's are green.
Having seen many advertisement involving green M&M's, I claim that more than 1/6th of all M&M's are green since the company is trying to push the green M&M character.
We seek to to test this hypothesis. What are the null and alternative hypothesis? Is it one-tailed or two-tailed? What is our sampling distribution?
- Carry out the test of the above hypothesis with a significance level of 0.05 using both the critical value method and the P-value method. If you repeated it with significance 0.01, would you have the same conclusion?
Homework 8 Due Tuesday, November 10th. Histogram of Scores.
- Section 8-3 (pgs 407-412): 18, 30, 35, 36
- Section 8-4 (pgs 419-423): 12, 32, 34
- Section 8-5 (pgs 428-431): 9, 10, 14
Link to topics list, Updated November 5th. We will discuss on Tuesday, November 10th
Link to Solutions (Note: there is a small error, at the top of page 7 it should say the P-value is .0392)
Histogram of Scores
Homework 9 Due Tuesday, December 1st. Histogram of Scores.
- Section 9-2 (pgs 449-453): 12, 14, 17
- Section 9-3 (pgs 463-467): 8, 14, 26
- Section 9-4 (pgs 473-477): 14, 18, 20
- Section 9-5 (pgs 482-486): 12
Homework 10 Due Tuesday, December 8th. Histogram of Scores.
Link to the four data sets: comma separated values, excel file.
- Section 10-2 (pgs 510-516): 14, 15, 16
- Section 10-3 (pgs 527-531): 13, 16
- Section 10-4 (pgs 536-539): 17
For the following four data sets, calculate r, find the regression line, and graph the data with the regression line. Feel free to use technology for this exercise.
Link to topics list, Updated December 5th. We will discuss on Friday, December 11th
Note: There is an error on the Poisson formula. It will be fixed on the exam.
The final will be Thursday, December 17th in BP-002 (the same room we have class in).
Other Resources & Links
Opinions expressed here or implied by links provided, do not represent the official views of Tufts University. The appearance of hyperlinks does not constitute endorsement of all opinions contained within.