Introductory Statistics

Andrew Sánchez

Fall 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

**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 2-4)

**Section 3-2 (pg 93):**18, 22**Section 3-3 (pg 109):**44**Section 3-4 (pg 125):**16, 32- 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?

For these exercises, you may use a calculator, but should indicate how you arrived at your numerical values.

**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- 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!)**

**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- 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 Solutions

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- 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.

**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- 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?

**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- 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?

**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 Solutions (Note: there is a small error, at the top of page 7 it should say the P-value is .0392)

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

**Section 10-2 (pgs 510-516):**14, 15, 16**Section 10-3 (pgs 527-531):**13, 16**Section 10-4 (pgs 536-539):**17

Note: There is an error on the Poisson formula. It will be fixed on the exam.

The final will be

**Simpsons' Paradox by VUDLab**, a nice visualization of a famous example of Simpsons' Paradox occuring.**Bayes' Theorem Web applet**, a simple web tool for using Bayes' Theorem to determine inverse probability in the example discussed in class.**WolframAlpha: Computational Knowledge Engine**, an online calculator you may use on your homework to turn your expressions into numerical values.**Sampling Distribution applet**, a simple web tool for taking samples of random integers and getting the sampling distribution of sample means mean as discussed in class.**Binomial Approximation applet**, a tool for visualizing two approximations of the binomial distribution.

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