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Ch. 9 Notes – Confidence Interval Estimates for the Difference between Two Population
Parameters and Hypothesis Testing for Two Population Parameters
Section 9.2 Two population proportions
Declare your subscripts at beginning and stay consistent throughout the problem
Test statistic (p. 443) – uses pooled sample proportion (p-bar)
Confidence Interval Estimates (p.443) – use point estimate of the difference between the two
sample proportions and then add and subtract margin of error
Example 1: Suppose in a sample of 1800 African women, 684 have anemia. In a sample of
1500 American women, 345 women have anemia. Construct a 92% confidence interval estimate
for the difference in proportions of all African women with anemia and all women from the U.S.
with anemia.
Example 2: Test the claim that African women have a greater proportion of anemic women than
America at the 0.01 level of significance.
Section 9.3 Two independent means
Declare your subscripts at beginning and stay consistent throughout the problem
Independent or dependent samples (page 454)
Test statistic calculation (page. 455) – assume both population standard deviation are unknown
and unequal
Use the smaller degrees of freedom to find the t critical value (s).
Confidence Interval Estimates (p.456) – use point estimate of the difference between the two
sample means and then add and subtract margin of error
Example 1: Use a 0.05 level of significance, to test an engineer's claim that the old batteries last
less time than the new batteries. Suppose the company selects a simple random sample of 50
new batteries and 50 old batteries. The old batteries run continuously for 190.1 minutes with a
standard deviation of 25.7 minutes; the new batteries, 200.3 minutes with a standard deviation of
40.3 minutes.
Example 2: Construct a confidence interval for the difference of the two mean batteries time
lengths that is equivalent to the test in example 1 above.
Section 9.4 Two dependent (matched pairs)means
Notation, requirements and test statistic calculation (page 468)
Find the paired differences and that becomes the data set we look at.
Confidence Interval Estimates (p.469) – use point estimate of the mean difference in the sample
pairs and then add and subtract margin of error
Example 1: A random sample of 20 adults was obtained. Below is the data that was obtained by
weighing the subjects before and after they had taken the pill for one week. Test the claim that
this pill was effective in reducing weight at a 0.10 level of significance.
Example 2: Construct a confidence interval for the difference of the mean weights that is
equivalent to the test in example 1 above.
Section 9.5 Two population standard deviations (or variances)
Notation, requirements and calculation of test statistic (page 478)
F-distribution – Table A-5 - numerator and denominator degrees of freedom (sub 1 goes with
the group with the larger standard deviation)
Example 1: A random sample of 10 hot drinks from Dispenser A had a mean volume of 203 ml
and a standard deviation of 3 ml. A random sample of 15 hot drinks from Dispenser B had a
mean of 206 ml and a standard deviation of 5 ml. Test the claim that there is no difference in
the variability of the volume dispensed by the two machines at a 0.05 level of significance.