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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

  3. Calculating A random sample of 1433 cars showed that 388 of them were more than 10 years old. What is the ?

  4. Calculating 1000 likely voters were surveyed about their opinions on the war in Afghanistan. 520 voters thought that the US should withdraw from Afghanistan within a year. Find . Out of 855 voters, 530 said that the US should not get directly involved in the conflict in Libya. What is the ?

  5. 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

  6. Confidence Interval for p • Out of 1000 likely voters, 520 supported withdrawing UStroops from Afghanistan. Construct a 99% confidence interval. Step 1: Find the point estimate for p. = 0.52 Step 2: Find Step 3: Check to see if np 5 and nq  5 1000(0.52)  5 and 1000(0.48)  5, so the sampling normal.

  7. Step 4: The maximum error of estimate, E. Step 5: Construct the confidence interval. 0.52 – 0.031 < p < 0.52 + 0.031 0.489 < p < 0.551 With 95% confidence, you can say the proportion of US voters that want the US to withdraw from Afghanistan is between 0.489 and 0.551.

  8. 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.

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

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

  11. With no preliminary estimate, use 0.5 for 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 accurate to within 2% of the population proportion. = You will need at least 4161 for your sample.

  12. 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= 2992 for your sample.

  13. 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?

  14. Class work #1 1. 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. 2. 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. 3. 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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