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Confidence Intervals for Population Proportions

Confidence Intervals for Population Proportions. The point estimate for p , the population proportion of successes, is given by the proportion of successes in a sample. (Read as p-hat). is the point estimate for the proportion of failures where.

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Confidence Intervals for Population Proportions

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  1. Confidence Intervals forPopulation Proportions The point estimate for p, the population proportion of successes, is given by the proportion of successes in a sample (Read as p-hat) is the point estimate for the proportion of failures where If and the sampling distribution for is normal.

  2. Confidence Intervals for Population Proportions The maximum error of estimate, E, for a x-confidence interval is: A c-confidence interval for the population proportion, p, is

  3. Confidence Interval for p In a study of 1907 fatal traffic accidents, 449 were alcohol related. Construct a 99% confidence interval for the proportion of fatal traffic accidents that are alcohol related. 1. The point estimate for p is 2. 1907(.235)  5 and 1907(.765)  5, so the sampling distribution is normal. 3.

  4. Confidence Interval for p • .235 In a study of 1907 fatal traffic accidents, 449 were alcohol related. Construct a 99% confidence interval for the proportion of fatal traffic accidents that are alcohol related. Left endpoint Right endpoint ) ( .21 .26 0.21 < p< 0.26 With 99% confidence, you can say the proportion of fatal accidents that are alcohol related is between 21% and 26%.

  5. Minimum Sample Size If you have a preliminary estimate for p and q, the minimum sample size given a x-confidence interval and a maximum error of estimate needed to estimate p is: If you do not have a preliminary estimate, use 0.5 for both .

  6. Example–Minimum Sample Size You wish to estimate the proportion of fatal accidents that are alcohol related at a 99% level of confidence. Find the minimum sample size needed to be be accurate to within 2% of the population proportion. With no preliminary estimate use 0.5 for You will need at least 4415 for your sample.

  7. Example–Minimum Sample Size You wish to estimate the proportion of fatal accidents that are alcohol related at a 99% level of confidence. Find the minimum sample size needed to be be accurate to within 2% of the population proportion. Use a preliminary estimate of p = 0.235. With a preliminary sample you need at least n= 2981 for your sample.

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