Inferences From Two Samples

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Chapter 9

• Inferences From Two Samples

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Section 9.2Inferences About Two Proportions

• In this section well be learning appropriate
  methods for using sample data to compare two
  population proportions/percentages.

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Assumptions

• 1. We have proportions from 2 simple random
  samples that are independent.
• 2. For both samples, the conditions np gt 5
  nq gt 5 are satisfied ? there are at least 5
  successes and 5 failures in each of the samples.

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• For hypothesis testing, we will use the same
  methods previously learned, with the following
  test statistic for 2 proportions (with HO p1
  p2)
• where,

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Example 1

• The lottery commissioners office in a state
  wanted to find if the proportion of men and women
  who play the lottery are different. A sample of
  500 men taken by the commissioners office showed
  that 160 of them play the lottery often. Another
  sample of 300 women showed that 66 of them play
  the lottery often. Testing at the 1
  significance level, can you conclude that the
  proportions of all men and all women who play the
  lottery often are different?

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Example 2

• In a study of women and coronary heart disease,
  the following sample results were obtained
  Among 10,239 women with a low level of physical
  activity (less than 200 kcal/wk), there were 101
  cases of coronary heart disease. Among 9877 women
  with physical activity measured between 200 and
  600 kcal/wk, there were 56 cases of coronary
  heart disease. Use a 0.05 significance level to
  test the claim that the rate of coronary heart
  disease is lower for women with moderate levels
  of physical activity.

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