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.

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.

• 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.

• 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.

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.

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

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.