CHAPTER EIGHT by ert554898

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									   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. 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.
Sample Size: given c and E…
 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)
   Section 6.4
Confidence Intervals for
 Variance & Standard
      Deviation
Point Estimates
 Population variance is δ2
 The point estimate for variance is s2


 Population standard deviation is δ
 The point estimate for standard deviation
 is s.
The Chi-Square Distribution
(table #6) Chi-Square = X 2

 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 area on the table using
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.



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