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Section 6.3

Section 6.3. 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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Section 6.3

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  1. Section 6.3 Confidence Intervals for Population Proportions

  2. 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 np 5 and nq  5 , the sampling distribution for is normal. Confidence Intervals forPopulation Proportions *Short Cut: Look at your x. Is it greater than or equal to 5. Yes Then take n – x. Is it greater than or equal to 5. Yes If both are yes, then It is normal.

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

  4. 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. Step 1: Find the point estimate for p. = 0.24 Step 2: Find Step 3: Check to see if np 5 and nq  5 1907(.24)  5 and 1907(.76)  5, 457.68 1449.32 *Short cut: x = 449 n-x = 1458 The distribution is Normal Step 4: The maximum error of estimate, E.

  5. Step 5: Construct the confidence interval. 0.21 < p < 0.27 With 99% confidence, you can say the proportion of fatal accidents that are alcohol related is between 21% and 27%.

  6. 277 U.S. adults, in a survey of 1026 U.S. adults, would prefer to have a girl if they could only have one child. Construct a 95% confidence interval for the proportion of adults who say that they would prefer to have a girl if they could only have one child.

  7. Practice Of 1418 high school baseball players, 93 suffered an injury while playing the sport. Construct a 99% confidence interval for the population proportion.

  8. If you do not have a preliminary estimate, use 0.5 for both Minimum Sample Size

  9. Example-Minimum Sample Size With no preliminary estimate use 0.5 for • 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 accurate to within 2% of the population proportion. = You will need at least 4161 for your sample.

  10. 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 accurate to within 2% of the population proportion. Use a preliminary estimate of p = 0.24 With a preliminary sample you need at least n= 3036 for your sample.

  11. You are running a political campaign and wish to estimate, with 95% confidence, the proportion of registered voters who will vote for your candidate. What is the minimum sample size needed if you are to be accurate within 3% of the population proportion?

  12. A survey of 250 households showed 62 owned at least one • gun. Construct a 90% confidence interval for the proportion of • households that own at least one gun. • A survey of 2450 golfers showed that 281 of them are • left-handed. Construct a 92% confidence interval for the • proportion of golfers that are left-handed. • A pollster wishes to estimate the proportion of United States • voters who favor capital punishment. How large a sample is • needed in order to be 90% confident that the sample proportion • will not differ by more than 4%? • You are running a political campaign and wish to estimate, with • 95% confidence, the proportion of registered voters who will vote • for your candidate. What is the minimum sample size needed if • you are to be accurate within 7% of the population proportion? • Use a preliminary estimate of p = 0.62

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