HW8_skeleton

9.1

• 1. Point estimate
• 2. Level of confidence; (1-??) x 100% [or (1-alpha) x 100%]
• 3. False, a 95% confidence interval means that 95% of intervals will contain the parameter if a large number of samples is obtained.
• 4. Critical Value
• 5. Increases
• 6. Decreases
• 7. 1.645
• 8. 2.575
• 9. 2.326
• 10. 1.75
• 11. p-hat = (0.201+0.249)/2 = 0.225. E = (0.249-0.201)/2 = 0.024. x = 0.225x1200 = 270
• 12. p-hat = (0.051+0.074)/2 = 0.0625. E = (0.074-0.051)/2 = 0.0115. x = 0.0625x1120 = 70
• 15. p-hat = 30/150 = 0.2. Lower bound = 0.2 - 1.645 x ???((0.2(100.2)))/150) = 0.146. Upper bound = 0.2 + 1.645 x ???((0.2(100.2))/150) = 0.254.
• 16. p-hat = 80/200 = 0.4. Lower bound = 0.4 - 2.33 x ???((0.4(1-0.4)))/200) = 0.319. Upper Bound = 0.4 + 2.33 x ???((0.4(1-0.4)))/200) = 0.481.
• 1. This statement is flawed because no interval has been provided about the population proportion.

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

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

  4. The statement is flawed because this interpetation suggests that this interval sets the standard for all the other intervals which isn’t true.

• 1. p-hat = 417/2306 = 0.181

  2. n(pHat)(1-(pHat)) = 2306 x 0.181(1-0.181) = 341.84… 341.84 ??? 10. Therefore the sample is less than 5% of the population.

  3. 0.181 - 1.645 x ???((0.181(1-0.181))/2306) = 0.168 is the Lower Bound. 0.181 + 1.645 x ???((0.181(1-0.181))/2306) = 0.194 is the Upper Bound.

  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. p-hat = 417/2306 = 0.430

  2. 496 x (0.430)(1-0.430) = 121.57… 121.57 ??? 10. Therefore the sample is less than 5% of the population.

  3. 0.430 - 1.96 x ???((0.430(1-0.430))/1153) = 0.401 is the Lower Bound. 0.430 + 1.96 x ???((0.430(1-0.430))/1153) = 0.459 is the upper bound.

  4. We are 95% confident that the population proportion of workers and retirees with less than $10,000 in savings is between 0.401 and 0.459.