Hw7_skeleton

8.2

• 1. 0.44
• 2. Sample proportion, x/n
• 3. False
• 4. True
• 5. The sampling distribution of p hat is approximately normal when n is less than or equal to 0.05N and np(1-p) is greater than or equal to 10.
• 6. The standard deviation of p hat decreases as the sample size increases. If the sample size increases by a factor of 4, the standard deviation of p hat remains the same.
• 7. The sampling distribution of p hat is approximately normal with Mu p hat = 0.4 and sigma p hat = square root 0.4(0.6)/500 is approximately equal to 0.022
• 8. The sampling distribution of p hat is approximately normal with Mu p hat = 0.7 and sigma p hat = square root 0.7(0.3)/300 is approximately equal to 0.026
• 1. The sampling distribution of p hat is approximately normal with Mu p hat = 0.35 and sigma p hat = square root 0.35(0.65)/1000 is approximately equal to 0.015

  2. P(p hat is great than or equal to 0.39) = 0.0040. About 4 out of 1000 random samples of size n = 1000 will result in 390 or more individuals, 39% or more, with the characteristic

  3. P(p hat is less than or equal to 0.32) = 0.0233. About 2 out of 100 ranodm samples of size n = 1000 will result in 320 or fewer individuals (32% or less) with the characteristic

• 1. The sampling distribution of p hat is approximately normal with Mu p hat = 0.42 and sigma p hat = square root 0.42(0.58)/1460 is approximately equal to 0.129

  2. P(p hat is great than or equal to 0.657) = . About 4 out of 1000 random samples of size n = 1000 will result in 390 or more individuals, 39% or more, with the characteristic

  3. type answers here.

• 1. The sampling distribution of p hat is approximately normal with Mu p hat = 0.39 and sigma p hat = the square root of 0.39(0.61)/500 is approximately equal to 0.022

  2. P(p hat is less than 0.38 = 0.3228). About 32 out of 100 random samples of size n = 5– adult Americans will result in fewer than 190 individulas (less than 38%) who believe that marriage is obsolete

  3. P(0.40 is less than p hat is less than 0.45) = 0.3198. About 32 out of 100 random samples of size n = 500 adult Americans will result in between 200 and 225 individuals (between 40% and 45%) who believe that marriage is obsolete.

  4. P(p hat is greater than or equal to 0.42) = 0.0838. About 8 out of 100 random samples of size n = 500 adult Americans will result in 210 or more individuals (42% or more) who believe that marriage is obsolete. This result is not unusual.