1. Making Inferences for Single Variables Chapter 11 Reading Assignment pp. 432-453

2. Terminology Point Estimate – a characteristic of a sample being used to estimate a population parameter Recall: population parameter is a statistical characteristic such as mean, median, mode or a percentage Confidence Interval – a range of values within a given point estimate is likely to fall; the confidence level specifies how likely it is that a point estimate will fall in a given range

3. Terminology 3 Recall: Std dev of sampling distribution of sample means—also called the standard error of the mean Formula 10.5 Follow ex for std error age; Skills 1, p. 435 Follow SPSS guide

4. 4 Chebyshev’s Rule: any sample, regardless of the f.d.shape It is possible that very few of the measurements fall within 1 std. Dev. Of the mean At least ¾ of the measurements will fall within 2 std dev of the mean (m-2s, m+2s) At least 8/9 of the measurements will fall within 3 std dev of the mean (m-3s, m+3s)

5. 3 Empirical Rule –frequency distributions are mound shaped Apprx. 68% of the measurements will fall within 1 std dev of the mean (m-s, m+s) Approx. 95% of the measurements will fall within 2 std dev of the mean (m-2s, m+2s) Essentially all the measurements will fall within 3 std dev of the mean (m-3s, m+3s)

6. Confidence Intervals and Levels 4 Where is the population mean? Can narrow the range of possibilities if it is assumed: 1. The sampling distribution of the means is normal 2. At least one of the means in the sampling distribution of sample means is identical to the population mean Hence, can infer that 95% of all possible sampling means in the sampling distribution fall within the range 44.16 to 45.40 (i.e. w/in 2 std dev) Picture, p. 438

7. Confidence Intervals and Levels 4 To construct confidence interval, need: The standard error for the mean (std dev of samp dist of samp means) Mean for a particular sample (to represent the mean of the sampling distribution of the sample means) 95% of all values in a normal distribution will fall within 2 standard errors of the mean. Therefore, 5% of the sampling values fall outside that range Skills 3, p. 440 SPSS—conf. Int (p. 441) P. 442-43—Interpretation of Confidence Interval

8. Z_(a/2) is the Z value with an area a/2 to its right (a=100-CI%) Confidence interval formulas, p. 445 Example, p. 445 Skills 4 Confidence levels using SPSS P. 446 P.449-50—standard Error of proportions ; formula 11.2, example P. 451 CI for specified levels: formula 11.3, example Skills 5, skills 6,skills 7

9. Homework –Chapter 11 Gen ex P. 461/ 1,3,4,6,9,11,13 Hand in: p. 462/ 8, 12; SPSS/ 1