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 6.2: # 1-27 odd, 29, 30, 35, 37, 39, 43, 45, 47, 49;
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 started a discussion of Sampling Distributions from Section 8.1 – we will discuss them in more detail on Wednesday. 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 next homework assignment is due on Monday, 2 November 2009 and consists of the following:

Section 6.2: # 1-27 odd, 29, 30, 35, 37, 39, 43, 45, 47, 49;
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’;
*** Use NRMHST program on the TI83/84;
**** To find the values z_α, use invnorm with area 1–α;
***** Recall, area under the probability density function is the same as the probability.

Monday, 19 October 2009

Today, we discussed binomial probability from Section 6.1. Then we discussed some of the previously discussed concepts that you will need to remember for this Chapter. 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 6.2: # 1-27 odd, 29, 30, 35, 37, 39, 43, 45, 47, 49;
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

Today, 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

Use graph paper for your graphs. For Section 6.2, we used the TI83/84 calculator function (see http://stats.jjw3.com/math1431/ti83binProb.htm) to calculate the binomial probabilities. 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, we will cover a few more examples of binomial probabilities. Also, 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.

Test 2 Correction

Chapter 4 will not be on Test 2 for Math1431 Section 160 (i.e., the class that meets at 5:30 p.m. – this parenthetical note is for the students who read the wrong blog).