Hw7_skeleton

8.2

• 1. 0.44
• 2. sample proportion, x/n
• 3. F
• 4. T
• 5. n<=0.05N and np(1-p)>=10
• 6. the sample size will decrease/the standard deviation will be halved
• 7. the sampling distribution of p-hat is approximately normal with mu p-hat=0.4, and sigma p-hat=0.022
• 8. the sampling distribution of p-hat is approximately normal with mu p-hat=0.7, and sigma p-hat=0.026
• 1. the sampling distribution of p-hat is approximately normal with mu p-hat=0.35, and sigma p-hat=0.015

  2. z=(p-hat - mu p-hat)/sigma p-hat=(0.39-0.35)/0.015=2.67 p(p-hat<0.39)=0.9962 1-p(p-hat<0.39)=p(p-hat>0.39)=0.0038

  3. z=(p-hat - mu p-hat)/sigma p-hat=(0.32-0.35)/0.015=-2 p(p-hat<0.32)=0.0228

• 1. the sampling distribution of p-hat is approximately normal with mu p-hat=0.42, and sigma p-hat=0.013

  2. z=(p-hat - mu p-hat)/sigma p-hat=(0.45-0.42)/0.013=2.31 p(p-hat<0.45)=0.9896 1-p(p-hat<0.39)=p(p-hat>0.39)=0.0104

  3. z=(p-hat - mu p-hat)/sigma p-hat=(0.4-0.42)/0.013=-1.54 p(p-hat<0.32)=0.0618

• 1. the sampling distribution of p-hat is approximately normal with mu h-hat=0.39, and sigma p-hat=0.022

  2. z=(p-hat - mu p-hat)/sigma p-hat=(0.38-0.39)/0.022=-0.46 p(p-hat<0.38)=0.3228

  3. z40=(p-hat - mu p-hat)/sigma p-hat=(0.4-0.39)/0.022=0.46 p(p-hat<0.4)=0.6773 z45=(p-hat - mu p-hat)/sigma p-hat=(0.45-0.39)/0.022=2.73 p(p-hat<0.45)=0.9968 P(0.4<p-hat<0.45)=p(0.45)-p(0.4)=0.9968-0.6773=0.3195

  4. p-hat=210/500=0.42 z=(p-hat - mu p-hat)/sigma p-hat=(0.42-0.39)/0.022=1.36 p(p-hat<0.42)=0.9131 P(p-hat>0.42)=1-P(p-hat<0.42)=1-0.9131=0.869 the result is not unusual