# 158 Calendar

All RED dates are unofficial entries and are subject to change. All BLACK dates are official entries.

“That’s the funny thing about practice. For days and days, you make out only fragments of what to do. And then one day you’ve got the whole thing. Conscious learning because unconscious knowledge, and you cannot say precisely how.”

From surgical resident Atul Gawande’s article “The Learning Curve,” published in the January 28, 2002 issue of The New Yorker.

### August 30

Find the web site (http://www.oswego.edu/~srp/stats). Once there choose "General course information" and locate the syllabus and calendar(s). Take a look at the Frequently Asked Questions at the bottom of the syllabus; examine the instructor’s responses at http://www.oswego.edu/~srp/stats/faqiaq.htm (these are only available on the internet). These detail the instructor's expectations.

Here’s theThe “formula” we discussed is simply the reciprocal of the square root of n.

Read the syllabus. Locate the syllabus,  course calendar and FAQs on the internet.

Read sections 1.1-1.3 through the middle of page 13.

Practice exercises:

·        Exercises 1.1-17.

·        Exercises Chapter 12: 12.16. 12.22, 12.23 use the chart and, if appropriate, formula to obtain the desired error margin. Question 8 page 636 – use the formula provided in class to obtain the error margin, then compare your result to the error margin of 4.7% given in the exercise. (I’m curious why the book has what appears to be an incorrect value here.)

Write up to hand in 9/1

1.      Without using the chart, explain why a result of 20% and a result of 80% must have the same error margin.

2.      Use your chart to explain to someone why the formula fails to produce a good approximate error margin for results outside the vicinity of 50%.

3.       Identify two factors that impact the error margin. For each write one sentence describing the relationship between that factor and the error margin.

1.      Consider a poll where there are only two candidates and everyone has an opinion (no undecided voters). Suppose Candidate A is at 80% +/- 3% (or whatever). This mean that we’re 95% confident that in the election A will get between 77% and 83% of the vote. Of course, with B the only other choice, B must get between 23% and 17% - or 20% +/- 3%. The error margin must be the same because any error made in computing the percentage “FOR” is equivalent to an error of the same amount in a different direction in computing the percentage “AGAINST.”

2.      You were told in class that the formula is appropriate for results near 50%. (In fact, the formula is nearly perfect for results of exactly 50%.) Pick any sample size and locate the two curves. From the chart it is clear that the error margin changes very little as the percentage ranges around 50%. So – one formula can handle all these situations. But, further to the left of the chart – where the percentage is either high or low – the error margin clearly begins to shrink. Because of this, the formula can’t work for high or low values of the percentage.

3.      The two factors are: The sample size. A larger sample sizes leads to a smaller error margin; The % (although in the 50% area it doesn’t matter much). Results further away from 50% have smaller error margins.

### September 1

Chapter 2 is assigned as reading.

Practice exercises in Chapter 2: 1 – 9.

Bring a calculator to class.

There was a Mini-homework. Everyone was awared 10 points out of 10 for it.

### September 3

Our initial data set – waits between eruptions of Old Faithful (the third column of the data set).

As of today we’ve covered through section 2.5.

Practice exercises in Chapter 2: 43, 50, 51, 76-81. Page 84 #13.

There was a pop quiz. Your paper is scored on the basis of your true achievement. However, because some people took it on their first day of class (just registered), everyone who took it was “curved” to 5 points.

### September 8

Read 3.1 – 3.4. We will only use the “defining formula” for standard deviation.

Practice exercises Chapter 3: 5, 7, 8, 24-27, 37, 38, 40, 41, 43, 53, 55, 59, 60, 65, 67, 69

Ignore any exercise asking you to use the “computing formula” for the standard deviation.  Be able to: Use the defining formula for a small data set; understand how the computation results in a reasonable measure of spread; use your statistics functionality on your calculator to compute it for a larger data set.

Be able to hand draw a boxplot. We will not worry too much about the details of creating a modified boxplot – but you should understand what the modified boxplot adds to the standard version.

The 11:30 section (that usually meets in 125 Snygg) will meet in 215 Snygg on Friday. This room is just off the NE stairwell of Snygg, above the snackbar.

### September 10

Here’s the states data we’ll look at in class.

Here’s a link for the data for the assignment due to hand in on Wednesday 9/9:

http://media.pearsoncmg.com/aw/aw_deveaux_introstats_1/data/text/dv01_05_37.txt

You’ll need to see the instructor for a copy of the assignment.

No new practice exercises nor reading

### September 13

Here’s a link to the data for the resistance exercise done in class. The given data produces the first histogram. The 19th observation is -2.92327; changing this to -4.9327 creates the second and third histograms. Changing it to +2.92327 creates the fourth.

Homework distributed Friday is  due Friday 9/18 – not Wednesday.

Office hours in 215 Snygg Lab (above Snygg Snacks) Mon 4 – 6 and Wed 3 – 5

We’ll probably do more in-class exercises next time, and move into Chapter 3.

### September 15

Handout in class. (Document in MS Word  format. Right click, “Save As” and save the document to your desktop. Bring the correct answers to class on Monday. Data sets from the handout in class: histobox2.txt and twohists.txt. Using these you can check your “guesses” and be sure to be correct.

### September 20

Section 3.5 is not assigned.

Practice (review) exercises. Pages 83-4:  1, 9-11, 13, 17, 19, 20, 23ab. Pages 140-2: 1, 2, 4, 6, 8, 18.

Section 4.1 is assigned as reading. That’s about all that we cover in Chapter 4.

Practice Exercises, Chapter 4 Section 1: 5-7, 9-12.

### September 22

Section 5.1-2 is assigned as reading.

Practice Exercises, Chapter 5:. 3, 4, 7, 9, 17a, 18a.

Histogram Matching Exercise (Word document). First try to compare attributes (mean, median, range, IQR, stdev) by inspection of the histograms only. Then check your results. This is assigned for Friday. Here’s a link to the data set for the exercise.

Also a worksheet on discrete random variables.

### September 24

We worked in class on the worksheet on discrete random variables. Complete it, if you haven’t in class.

There was a pop quiz. While it’s scored on a 20 point basis, it’s in the grade book on a 5 point basis. To get your score out of 5 divide the mark on your paper by 4.

### September 27

The assignment should be returned. It is scored out of 15 points.

Friday’s pop quiz was scored on a 20 point basis, but it’s in the grade book on a 5 point basis. To get your score out of 5 divide the mark on your paper by 4.

Read Section 5.3 thru the bottom of page 241.

Practice 25-29, 33-40.

Exam Friday. Coverage is detailed above:

·        Chapter 1 Sections 1, 2, 3 through the middle of page 13

·        Chapter 2

·        Chapter 3 sections 1 – 4

·        Chapter 4 section 1

·        Chapter 5 sections 1 – 3

·        Materials distributed and discussed in class with one exception (see below).

·        Not covered is the chart and formula relating to polls that we covered on the first day of class (we’ll get back to this later in more detail). See the purple text in the August 30 entry.

### September 29

We’ll do some exercises with binomial random variables in class.

My office hours Thursday begin at noon. I’ll extend them to around 3:30.

Exam guidelines. Unless otherwise stated, these guidelines are in force for the entire semester.

·        Bring a calculator, pencils and eraser.

·        You may bring one 3 by 5 inch card or piece of paper with anything you like on it. Larger cards or sheets are unacceptable.

·        If you must leave to use the bathroom, alert the instructor and obtain an OK. Cover your work as you leave.

·        The instructor will alert you with 5, 2 and 1 minute warnings. When time is up the instructor will leave the room. If your paper is not submitted at the time, you will get no credit.

·        Pay attention to your own workspace only. There may be multiple versions of the exam. Copying another’s answers will identify you and lead to many mistakes.

·        On rare occasions health concerns or an emergency will force someone to miss an exam period. If this happens to you: It is assumed that upon the next class day you will have documented the episode and will be prepared to take the exam immediately. You may also be asked to take the exam as an oral exam.

### October 1

Exam 1. See above for coverage (9/27) and guidelines (9.29).

### October 4

Picture of the normal curve. (You can copy, paste, and replicate it.) These pictures accompanied a handout on the standard normal distribution.

Practice exercises chapter 6: 3-6, 21, 24, 25, 29, 31, 33, 35, 37, 41.

### October 6

Practice exercises chapter 6: 39, 40, 47, 49, 51, 53, 57

Answers to 40: a) 1.88, b) 2.575.

### October 8

Read Section 6.5. Normal approximation for binomial distributions. (Relates to Section 5.3.)

Practice exercises Section 6.5: 76, 77, 81, 83.

Homework – due next Friday – was assigned. See the instructor for a copy. Here’s the data for the homework.

www.oswego.edu/~srp/stats/histmat1.txt

www.oswego.edu/~srp/stats/comp1f04.txt

Note: The value 1442 appears twice (pages 2 and 4). Replace it with 1422. Here’s a link to the document that shows you how to compute z-scores and figure out things like “how many are between -1 and +1.”

www.oswego.edu/~srp/stats/MTB/Standard.htm

### October 11

A student assistant will be in the Math lab (above Snygg Snacks) to help you with the computing for the second assignment. Hours Tuesday: 2:15 – 4:00.

Read Section 6.5. Normal approximation for binomial distributions. (Relates to Section 5.3.)

Practice exercises Section 6.5: 76 - 83, 85, 86ab.

76) The formula is too cumbersome to use for large n.

78) a) 0.4512, 0.8907 b) 0.8858, 0.6255 – 0.1711 = 0.4544.

80) The mean is 6.72, stdev 2.376; a)  z = -0.51 and -0.93; probab = 0.1288; b) The z’s are 1.32 and 0.75. The probability is 0.1332; c) At least 1 gives a z = (0.5 – 6.72)/ 2.376 = -2.62, the prob is 0.0044 = 1 in 227; d) At most two gives z = (2.5-6.72)/2.376 = -1.78. The probability is 0.0375.

82) The mean is 131.75; stdeve = 7.894. a) Exactly half is exactly 125. Find z scores for 124.5 and 125.5, z = -0.92 and -0.79. The area between these (= prob) is 0.2148 – 0.1788 = 0.0360 (about 1 in 28 times); b) At least 125. Use 124.5, z = -0.92 for a prob 0.8212. c) Use 114.5 and 130.5, z = -2.19 and -0.16. The prob is 0.4364 – 0.0143 = 0.4222.

84) Here p = 1/15000. a) With n = 10000, the expected number is np = 10000(1/1500) = 6.667. (The standard deviation is 2.581.) b) More than 7, use 7.5 for a z = 0.32. The prob is 0.3745; at most 10 use 10.5, z = 1.49, the prob is 1 – 0.0681 = 0.9319.

### October 13

A student assistant will be in the Math lab from 4:30 to 6 Thursday. I will be available there (or in my office) from 3:30 – 4:30 today (Wed) and noon to 2 Thursday.

Practice Review exercises Chapter 6: 3, 6, 7, 17, 19-24.

6) a) TRUE, b) TRUE

20) a) 0.8944 – 0.0606 = 0.8338. b) 0.8944. c) 0.9946.

22) a) Q1 = 500 – 0.67(100) = 567; Q3 = 500 + 0.67(100) = 567. The 99th percentile is 500 + 2.33(100) = 733.

24) a) With n = 1500 and p = 0.80 the mean is 1200 and standard deviation is 15.49. Exactly 1225 means between 1224.5 and 1225.5 . The z-s are 1.58 and 1.65. The probability is approximately 0.9505 – 0.9429 = 0.0076 (about 1 in 132). c) Use 1174.5 for z = -1.65. The probability is approximately 0.0495. c) 1149.5 to 1250.5 gives z = +/-3.26; the prob is 0.9994 = 0.0006 = 0.9988.

84) Here p = 1/15000. a) With n = 10000, the expected number is np = 10000(1/1500) = 6.667. (The standard deviation is 2.581.) b) More than 7, use 7.5 for a z = 0.32. The prob is 0.3745; at most 10 use 10.5, z = 1.49, the prob is 1 – 0.0681 = 0.9319.

### October 18

Assignment distributed. It is due next Monday.

Practice exercises 30-33, 35a, after section 7.2.

Practice exercises 41-55 odd, 46-52 even, after section 7.3.

Section 7.1 is a lot of talk and an artificial example. The example is similar to the one done in class on Friday (tossing multiple dice).

Go over book’s boxes from Sections 7.1, 7.2 and 7.3.

### October 20

Practice exercises 41-55 odd, 46-52 even, after section 7.3.

### Emergencies sometimes cause someone to miss an exam. If this happens to you, you are expected to show up ready to take the exam the next class day. You may be asked to take an oral exam. You are expected to visit the course calendar online in case of any other announcements.

Assignment distributed. It is due next Monday.

Midterm 2.

### November 1

Practice exercises in chapter 8: 35-37,39, 41-45, 46a, 47, 48, 49.

36) 6.8. 52.8 +/- 3.4 which is 49.4 to 56.2.

42) 151.6/2 = 75.8.

44) a) 14.6. b) In 95% of all samples, the estimate differs from the parameter by no more than 14.6. c) (2.576*42/12)^2 = 81.29 round up to 82. (The symbol ^ means “raised to the power.) d) the CI would be 36.2 +/- 12: 24.2 to 38.2.

46. (1.96*13.36/2)^2 = 171.42 round up to 172.

48. a) 9.8. b) 4.9. c) 2.45.

### Practice exercises: 56-60, 63-66,

The assignment (MS Word format)

The data set.

Guidance on using Minitab to get 1-sample confidence intervals using the t method.

Guidance on using Minitab to randomly select data from a column.

### November 10

Midterm 2 Retake.

### December 1

Exam Friday. Sections 8.3, 8.4,  9.1, 9.2, 9.3, 9.5, 9.6, 12.1 (especially sample size determination), 12.2..plus assignments and amterials from class.

Allowed one 3 by 5 notecard (both sides OK). Absolutely no exceptions. Please – if you write it on a large sheet, cut it out before starting the exam.

Bring pencils, erasers, and calculators.

Obviously no access of cell phones, etc.

Tables will be provided for you.

Turn your paper over and raise your hand for permission to use the rest room. It will be granted (but may be delayed until others have returned).

Emergencies sometimes cause someone to miss an exam. If this happens to you, you are expected to show up ready to take the exam the next class day. You may be asked to take an oral exam. You are expected to visit the course calendar online in case of any other announcements.

There will be no retake opportunity.

The final “graded” assignment is available. It is due on the final day of class. It is not available online – see the instructor if you need a copy.

### December 3

Midterm 3.

Solutions to the problems handed out in class.

1. While it’s possible to construct a confidence interval, it’s silly to do so. What population mean are you estimating? This is not a random sample from any population.

2. The sample mean is 577.5 with stdev 73.058. The test statistic is (577.5 – 500)/(73.058/sqrt(6)) = 2.60. The P-value is bounded between 0.01 and 0.025 (Look at the 5 DF row of the T Table). It’s very close to 0.025 – and in fact is exactly 0.024. This rejects the null hypothesis at the 5% level, but not the 1% level. There is strong evidence supporting the alternative hypothesis. The 95% CI uses t = 2.571: 577.50 +/- 2.571*(73.058/sqrt(6)) which is 577.05 +/- 76.67 or from 500.8 to 654.2. You should not use either of these inference procedures (test or CI) for small samples from nonnormal populations.

3. H0: p = 1/3  HA: p > 1/3. The test statistic is (55/120 – 1/3)/sqrt((1/3)*(2/3)/120) = 0.12500/0.0430331 = 2.905. Use the Z table to find the P-value = area right of 2.905 (2.91 is fine): 0.0019 is the P-value. The result is statistically significant at the 5% level – and at the 1% level. There’s very strong evidence supporting the alternative (which is the theory that some people are not guessing, and can actually discriminate). Since 40 of 120 should guess right by luck alone, of the remaining 80 people, 15 have a correct answer. 15/80 = 0.1875 = 19% (rounded properly).

### December 6

Here’s the document that was posted to help you with the assignment: Guidance for Minitab 1 sample T-tests

I handed out the “textbook” for the final week. The document contains the material and exercises for the remainder of the semester. This material roughly goes with Chapter 12, Section 3 of the textbook.

### December 8

Instructor evaluation day. A handout (using graphs to assess tests and error margins of intervals).

### December 10

Final wrap up. All assignments are due – solutions will be discussed and or distributed.

### Correction!

On the CECR document – the solutions to #5 have two errors (haste makes waste)

The display of results was copied and pasted from #4, but I never changed the figures. And – I switched the digits around in the error margin (from 7.5% to 5.7%). Here are the correct solutions to #5:

This is a properly randomized observational study. Results should be tabulated as follows

 % of refusals # people surveyed Location Central-City 28.9 294 Non-Central-City 17.1 1015

p1 would be the proportion of all central-city residents who refuse. The 99% confidence interval is 11.8% ± 7.5%. You are 99% confident that the refusal rate among all central-city residents is between 4.3% and 19.3% higher than for non-central-city residents. The difference (of 11.8%) is statistically significant at the 1% level.

Thanks to Ms. Chen, who noticed.

### Final Exam Information

Dec 15, 10:30 am, Snygg 125 Final Exam Section 810

Dec 17, 10:30 am, Snygg 101 Final Exam Section 800

The coverage is: “all of it.” Look above for September 27, October 27 and December 1 entries, where coverage for the midterms was detailed. In addition, include the material coverd on December 3, 6, 8 and 10.

You’re allowed one 8-1/2 by 11 (inch) sheet of notes (both sides OK).

Bring pencils, erasers, and calculators.

Obviously no access of cell phones, etc.

Tables will be provided for you.

Turn your paper over and raise your hand for permission to use the rest room. It will be granted (but may be delayed until others have returned).

There will be assigned seating. A seating chart will be posted on entrance doors. You must sit at your assigned seat. (Let me know if you need lefty considerations.)

Instructor’s Office Hours:

·        Dec 13 2 – 5 (check room 303, across the hall from 308).

·        Dec 14 2:30 – 5:30

·        Dec 15: 10:30 – 1:00 Snygg 125.

·        Dec 16: 2 – 5.