HW8_skeleton

9.1

• 1. point estimate
• 2. level of confidence, (1-α)(100%)
• 3. True
• 4. critical value
• 5. increases
• 6. decreases
• 7. 1.645
• 8. 2.575
• 9. 2.32
• 10. 1.75
• 11. p̂=0.225, margin of error= ±0.024, x=270
• 12. p̂=0.0625, margin of error= ±0.0115, x=70
• 15. (.146, .254)
• 16. (.320, .480)
• 21. Answer C and Answer D are the most reasonable interpretations of the survey results. Answer A does not mention the margin of error while Answer B incorrectly applies the margin of error on the level of confidence.
• 1. p̂=417/2306= 0.18

  2. 2306(0.18)(0.82)≥10 and sample is less than 5% of the population - Yes, the requirement for constructing a confidence interval about p are satisfied.

  3. 0.18 ± 1.645√[(0.18x0.82)/(2306)]=0.18 ± 0.0132 =(0.167,0.193)

  4. We are 90% confident that the population proportion of adult Americans aged 18 and older who have donated blood in the past two years is between 0.167 and 0.193.

• 1. p̂=496/1153=0.43

  2. 1153(0.43)(0.57)≥10 and sample is less than 5% of the population - Yes, the requirement for constructing a confidence interval about p are satisfied.

  3. 0.43 ± 1.96√[(0.43x0.57)/(1153)]=0.43 ± 0.0289 =(0.401,0.459)

  4. We are 95% confident that the population proportion of workers and retirees in the United States 25 years of age and older that have less than $10,000 in savings is between 0.401 and 0.459.