HW8_skeleton

9.1

• 1. Point Estimate
• 2. Level of Confidence
• 3. False. A 95% confidence interval means 95% of intervals will contain the parameter if a large number of samples is obtained.
• 4. Critical Value
• 5. Increases (as the level of confidence of a confidence interval increases, the margin of error increases).
• 6. Decreases (as the sample size used to obtain a confidence interval increases, the margin of error decreases).
• 7. Critical Value = 1.645 (1.645 comes from the fact that z sub 0.05 is the z-value such that 5% of the area under the standrard normal curve is to the right).
• 8. Critical Value = 2.575 (The 2.575 comes from the fact that z sub 0.005 is the z value such that 0.5% of the area under the standard normal curve is to the right).
• 9. Critical Value = 2.33. The 2.33 comes from the fact that z sub 0.01 is the z value such that 1% of the area under the standard normal curve is to the right).
• 10. Critical Value = 1.75. (The 1.75 comes from the fact that z sub 0.04 is the z value such that 4% of the area under the standard normal curve is to the right).
• 11. Required population proportion: 0.45/2 = 0.225, required margin of error is 0.024, required x value is 270. Final Answer: 270.
• 12. Point estimation of the population: p-hat = 0.0625, margin of error = 0.0115, and x = 70. Final Answer: 70.
• 15. Required Confidence Interval is: Lower bound: 0.146 and Upper bound = 0.254
• 16. (0.319, 0.481)
• 1. The statement is flawed because no interval has been provided about the population proportion.

  2. The statement is flawed because this interpretation has a varying level of confidence.

  3. The statement is correct because an intrval has been provided for the population proportion.

  4. The statement is flawed because this interpretation suggests that this interval sets the standard for all the other intervals, which is not true.

• 1. P-hat = 417/2306 = 0.181

  2. 2306x0.181(1-0.181); The =341.84 ≥ 10 sample is less than 5% of the population.

  3. Lower bound = 0.168. Upper bound = 0.194

  4. We are 90% confident that the population proportion of adult Americans 18 years and older who have donated blood in the past two years is between 0.168 and 0.194.

• 1. The population proportion = 0.15

  2. Sample proportion = 0.430. Then calculate np(1-p)=1153(0.430)(1-0.430) = 282.60 (≥10). The sample is less than 5% of the population.

  3. Lower bound: 0.402 and Upper bound is: 0.459

  4. We are 95% confidence that the population of works and retireers in the U.S., who are 25 years of age and/or older, who have less than $10,000 in savings, is between 0.402 and 0.459.