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MATH 1410/6.3 and 6.4

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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.
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)
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
2
(table #6) Chi-Square = X
 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-andleaf plot. Use a 99% level of confidence.
 Key: 3|4 = 3.4
3 469
4 689
5 134579
6 01
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