Monday, 23 November 2009

First, I hope everyone has a safe Thanksgiving Break.

Second, Test 5 will be on the last day of classes and will cover Chapter 10, Chapter 11, Section 1.3, Section 3.5, Section 4.2, Section 5.1, Section 6.2 and Section 7.3.

Third, to help you prepare for the cumulative Final Exam, here are some hand-picked problems from the textbook:

p. 51 # 26, 32;
p. 87 # 31 – construct a stem-n-leaf plot and describe the distribution only;
p. 100 # 4abcd;
p. 103 # 12cd;
p. 170 # 2;
p. 172 # 10abc;
p. 175 # 20;
p. 217 # 6abcd, 8acd;
p. 281 # 10, 14, 18;
p. 315 # 2, 12abcde;
p. 369 # 16, 26;
p. 370 # 30 – you are told to use the normal approximation;
p. 401 # 6 – ignore question about if the result is unusual;
p. 402 # 10 – ignore question about if the result is unusual;
p. 449 # 6;
p. 451 # 14;
p. 504 # 12;
p. 505 # 18;
p. 548 # 14, 22.

I encourage you to work with classmates to determine if your answers are correct.

Wednesday, 4 November 2009

Today we discussed Section 9.1 which concerned Confidence Intervals (CI) for population mean. It is important to know

1. how to calculate CI using the TI83/84 (and not by hand);
2. how confidence level and sample size affect CI;
3. how to interpret what a CI tells us about the parameter.

We will do many more calculations of CI over the next several class periods. Also, on Monday, we will discuss Sections 8.2, 9.2 and 9.3.

There is no homework due on Tuesday.

Wednesday, 28 October 2009

Important: Test 3 is on Monday, 2 November 2009 and will cover Chapters 6 and 7 and Section 8.1. You will need to know when and how to use the following calculations:

• binompdf(n, p, k)
• binomcdf(n, p, k)
• 1–binomcdf(n, p, k)
• normalcdf(x_lower, x_upper, μ, σ)
• normalpdf [hint: NEVER for this course!]
• invnorm(area to left, μ, σ)
• NRMHST
• when the normal approximation to binomial probability is permitted [np(1–p) ≥ 10]
• normal approximation to binomial probability [using μ = np and σ = sqrt(np(1–p)) and using appropriate values for x
• mean and standard deviation of sampling distribution
• 68-95-99.7 Rule for any normally-distributed set of data – including a sampling distribution
• finding z-score (i.e., z = (x-μ)/σ).

The test items will not be in any order with respect to the textbook. Question #1 on the test is: “State the Central Limit Theorem. Explain, in your own words, what this theorem states.” You will need to know the other material from these sections, not just the calculations.

Today, we discussed applications of the sampling distribution and the Central Limit Theorem (CLT). According to CLT, if given x~N(μ,σ), then the sample mean (x-bar) is also normally distributed with mean μ and standard deviation σ/sqrt(n). In fact, no matter what the shape of distribution of the population, the sampling distribution will always be approximately normal with mean μ and standard deviation σ/sqrt(n).

The next homework assignment is due on Monday, 2 November 2009 and consists of the following:

Section 7.3^*: # 1-11 odd, 17-25 odd;
Section 7.5: # 1-29 odd;
Section 8.1: # 1, 2, 3-15 odd, 17bc, 19-29 odd.

^* Ignore any questions involving percentiles.

Monday, 26 October 2009

Important: Test 3 is on Monday, 2 November 2009 and will cover Chapters 6, 7, and 8. You will need to know when to use

• binompdf(n,p,k)
• binomcdf(n,p,k)
• 1–binomcdf(n,p,k)
• normalcdf(x_lower,x_upper,μ,σ)
• normalpdf [hint: NEVER for this course!]
• invnorm(area to left,μ,σ)
• NRMHST
• when the normal approximation to binomial probability is permitted [np(1–p) ≥ 10]
• normal approximation to binomial probability [using μ = np and σ = sqrt(np(1–p)) and using appropriate values for x
• mean and standard deviation of sampling distribution

The test items will not be in any order with respect to the textbook.

Today, we briefly discussed, again, that the area under the normal curve refers to percentage and probability. Thus, you can use normalcdf to calculate area, percentage or probability. Recall, if z is used, then assume N(0,1). If given N(μ,σ), then the distribution is normal with mean μ and standard deviation σ.

We also discussed one example from Section 7.5 and how add or subtract 0.5 or both add and subtract 0.5 from x to make the correction for continuity (see Figure 47 on p. 363 of your text).

Lastly, we discussed Sampling Distributions from Section 8.1 – we will discuss them in more detail on Wednesday. At the very end of class I mentioned The Central Limit Theorem (CLT). This is so important to statistics that I require that you know the exact definition for the test (see p. 385 for a decent definition). We will finish discussing Chapter 8 on Wednesday. The sampling distribution applet that was used in class is located at http://onlinestatbook.com/stat_sim/sampling_dist/index.html.

The next homework assignment is due on Monday, 2 November 2009 and consists of the following:

Section 7.3: # 1-11 odd, 17-25 odd;
Section 7.5: # 1-29 odd;
Section 8.1: # 1, 2, 3-29 odd;
Section 8.2: # 1-21 odd.

Wednesday, 21 October 2009

Today, we discussed Sections 7.1, 7.2 and 7.4 and computed several examples.  The homework that is due on Monday, 26 October 2009 includes*:

Section 7.1: # 1-11 odd, 19-27 odd, 31, 33;
Section 7.2**: # 1-13; 16-21 all, 23, 27-29 odd, 33-43 odd, 45-49 odd;
Section 7.4: # 9, 11.

* Note: there are some changes from the last post!
** Use the appropriate TI83/84 function or program – make sure that you show the required ‘work’.

Monday, 20 October 2009

Today, we spent some time discussing homework questions from Chapter 6. Then we discussed some of the previously discussed concepts that you will need to remember for this Chapter. Finally, we discussed the normalcdf function for the TI83/84. We will cover several more ideas from Chapter 7 on Wednesday. Some of the homework that will be due on Monday, 26 October will include*:

Section 7.1: # 1-11 odd, 19-35 odd;
Section 7.2**: # 1, 3, 5bc, 7bc, 9bc, 11bc; 13-49 odd;
Section 7.3**: # 1-11 odd, 17-25 odd;
Section 7.4***: # 9, 11.

* More information will be given on Wednesday about exactly what will be due – it will depend on how much we cover on Wednesday;
** Use the appropriate TI83/84 function or program – make sure that you show the required ‘work’;
*** Use NRMHST program on the TI83/84.

Wednesday, 14 October 2009

In the last two class periods we covered Section 6.1 (Discrete Random Variables) and Section 6.2 (Binomial Probability Distribution).

The next homework assignment is due on Monday, 19 October 2009 and consists of the following:

Section 6.1: # 1, 3, 7, 8, 11, 16, 17, 19abcfg, 21abcef, 23abc, 25abc, 27, 28, 30
Section 6.2: # 1-27 odd, 29, 30, 35, 37, 39, 43, 45, 47, 49

Use graph paper for your graphs. You may use the calculator functions (see http://stats.jjw3.com/math1431/ti83binProb.htm) to calculate the binomial probabilities for the homework. Keep in mind what I expect for your work when calculating binomial probabilities, for example: binompdf(12,0.4,3)=0.142.

The next quiz is on Monday, 19 October 2009 and will cover finding binomial probabilities.

On Monday and Wednesday of next week, we will discuss most of Chapter 7 – recall that we already talked about most of these ideas in a previous section. We will use the following TI83/84 instructions:

How to find area under the normal curve: http://stats.jjw3.com/math1431/ti83norm.htm
How to find and graph the area under a normal curve: http://stats.jjw3.com/math1431/ti83normArea.htm
How to find a z-score given the area under a normal curve: http://stats.jjw3.com/math1431/ti83invNorm.htm
How to check if data is normally-distributed: http://stats.jjw3.com/math1431/ti83normHist.htm

If you have any questions regarding the homework before Monday, please stop by my office or email me – you can email me over the weekend.

Wednesday, 30 September 2009

Important Announcement: Test 2 will be on Wednesday, 7 October 2009 and will cover Chapter 4 and Chapter 5 and, maybe, some of Chapter 6.

Today, we discussed several additional rules of probability and practiced them with many examples. Please make sure that you remember each rule and know when to use each rule.

Here is a link to an applet that simulates the Monty Hall problem (a different one than was used in class): http://math.ucsd.edu/~crypto/Monty/monty.html – This applet keeps a record of everyone who has played the game, so that you can see the long-term [frequentist] probability.

Here is a link to an applet that simulates the Monty Hall problem (one that simulates Monty not knowing where the prize is): http://www.math.ucsd.edu/~crypto/Monty/montydoesnotknow.html This applet keeps a record of everyone who has played the game, so that you can see the long-term [frequentist] probability.

The next homework assignment (typically due on Mondays) will be collected on Wednesday, 7 October 2009 so that you can study from the assignment:

Section 5.1: # 9, 11, 15-33 odd, 37, 45, 47
Section 5.2: # 1-41 odd
Section 5.3: # 11, 12, 16*, 17*, 20*, 21*
Section 5.4: # 1–7 odd, 9-19* odd

* We will complete some examples similar to these during the next class.

Monday, 28 September 2009

Next Quiz on Wednesday, 30 September 2009 and will cover Section 5.1.

Today we covered Section 5.1 and discussed the three types of probability:

1. frequentist;
2. classicist;
3. subjective.

When we use a ‘fair’ coin or ‘fair’ die, then we can construct a sample space and use the classicist definition of probability. From Section 5.1, we discussed two rules of probability – the ones that are important for probability models. Lastly, from Section 5.2, we discussed the two addition rules and the complement rule for probability.

Next homework assignment consists of at least the following:

Section 5.1: # 9, 11, 15-33, 37, 45, 47
Section 5.2: # 1-41 odd

Wednesday, 23 September 2009

Reminder 1: Project 1 is due on Monday, 28 September 2009.

Reminder 2: Homework for Chapter 4 is due on Monday, 28 September 2009. See the previous post for details.

Today, the class completed Test 1. I will have the tests graded by Monday and they will be returned at the end of class on Monday.