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Inference About the Difference Between Population Proportions

Inference About the Difference Between Population Proportions. Section 10.5. Difference Between Population Proportions. Inference about parameter p 1 – p 2 uses the statistic p-hat 1 – p-hat 2 . Samples must be large and independent SRS’s.

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Inference About the Difference Between Population Proportions

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  1. Inference About the Difference Between Population Proportions Section 10.5

  2. Difference Between Population Proportions • Inference about parameter p1 – p2 uses the statistic p-hat1 – p-hat2. • Samples must be large and independent SRS’s. • Sampling Distribution of p-hat1 – p-hat2 is approximately normal for large samples. • Mean of sampling distribution of p-hat1 – p-hat2: p1 – p2 • Standard Deviation: √p1q1/n1 + p2q2/n2

  3. Confidence Intervals for 2 Proportions • To estimate p1 – p2 • (p-hat1 – p-hat2) ± z*sp-hat1 – p-hat2 • Example: Estimate the difference between the proportion of users of 2 toothpastes who will never switch brands. In a sample of 500 users of brand A, 100 will never switch. In a sample of 400 users of brand B, 68 will never switch. Construct a 97% confidence interval of the difference in population proportions.

  4. Hypothesis Testing About 2 Proportions • H0: p1 = p2 (since they are equal then we can pool the sample proportions). • St dev of p-hat1 – p-hat2 = √pq(1/n1 + 1/n2) • Test statistic z = • Example: Toothpaste. Can we conclude that there is a higher proportion of brand A users than brand B users who will never switch? • HATS

  5. Example: Sleep Problems • In 2001 69% of the 1600 adults surveyed had sleep problems. In 2005 75% of the 1506 adults surveyed had sleep problems. Did the percentage of adults with sleep problems change between 2001 and 2005? • HATS

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