Confidence Intervals for Population Proportions Section 6.3 Confidence Intervals for Population Proportions

Point Estimate for Proportions The Population Proportion is called p The Point Estimate is the sample proportion is called “p hat”

To find the Margin of Error, E

Confidence Intervals for the Population Proportion A c-confidence interval for the population proportion p is: – E < p < + E

Construct a C.I. for the Proportion 1. Find n and x to find 2. Make sure the normal approximation is allowed: and 3. Find the critical value zc that corresponds with the given level of confidence. 4. Find the margin of error, E. 5. Find the left and right endpoints and form the confidence interval.

14. In a survey of 4013 US adults, 722 say they have seen a ghost 14. In a survey of 4013 US adults, 722 say they have seen a ghost. Construct a 99% C.I. for the population proportion. 16. In a survey of 891 US adults who follow baseball in a recent year, 184 said the the Red Sox would win the World Series. Construct a 90% C.I. for the population proportion.

To find minimum sample size

20. You wish to estimate, with 95% confidence, the population proportion of US adults who say chocolate is their favorite ice cream flavor. Your estimate must be accurate within 5% of the population proportion. A) No preliminary estimate in available. Find the minimum sample size needed. B) Find the minimum sample size needed, using a prior study that found that 27% of US adults say that chocolate is their favorite ice cream flavor. C) Compare results from parts (A) and (B)

Confidence Intervals for Variance & Standard Deviation Section 6.4 Confidence Intervals for Variance & Standard Deviation

Point Estimates Population variance is σ2 The point estimate for variance is s2 Population standard deviation is σ The point estimate for standard deviation is s.

The Chi-Square Distribution (table #6) Chi-Square = X2 Use for sample sizes n > 1 All X2 > 0 Uses Degrees of Freedom: d.f. = n – 1 Area under the curve = 1 Chi-Square distributions are positively (or right) skewed

Finding Critical Values for X2 X2L is the LEFT hand critical value Find the area on the table using X2R is the RIGHT hand critical value

Find the critical values X2L & X2R 7. c = 0.95 n = 20 8. c = 0.80 n = 51

Confidence Interval for Variance

To find Confidence Intervals 1. Verify the population has a normal distribution. 2. Find degrees of freedom: d.f. = n – 1 3. Find point estimate s2 4. Find critical values using chi-square table. 5. Find the left and right endpoints for the C.I. for the population VARIANCE. 6. Square root to find the left and right endpoints for the C.I. for the population STANDARD DEVIATION.

10. You randomly select and measure the volumes of the contents of 15 bottles of cough syrup. The results (in fluid ounces) are shown. Use a 90% level of confidence. 4.211 4.264 4.269 4.241 4.260 4.293 4.189 4.248 4.220 4.239 4.253 4.209 4.300 4.256 4.290

16. The weights (in pounds) of a random sample of 14 cordless drills are shown in the stem-and- leaf plot. Use a 99% level of confidence. Key: 3|4 = 3.4 3 4 6 9 4 6 8 9 5 1 3 4 5 7 9 6 0 1