Hw7_skeleton

8.2

• 1. .44
• 2. sample proportion, x/n
• 3. False
• 4. True
• 5. p-hat is approximately normal when n ≤ .05N and np(1-p) ≥ 10
• 6. As the sample size increases, the standard deviation of p-hat decreases.If the sample size is increased by a factor of 4, the standard deviation of p-hat decreases.
• 7. p-hat sampling dist. is approximately normal with u sub p-hat=.4 and sigma sub p-hat= square root of .4(.6)/500=.022
• 8. p-hat sampling dist. is BLANK with u sub p-hat=.7 and sigma sub p-hat= square root of .7(.3)/300=.026
• 1. The sampling distribution of p-hat is approximately normal with mu sub p-hat=0.35 and sigma sub p-hat= square root of .35(.65)/1000= 0.015

  2. p(p-hat ≥ .39)=0.0040. About 4 out of 1000 random samples of n=1000 will lead to 390 or more individuals (≥39%) w/ the characteristic.

  3. p(p-hat≤.32)=0.0234. Around 2/100 random samples of n=1000 will lead to 320 or less people w/ the characteristic.

• 1. The sampling distribution of p-hat is approximately normal with mu sub p-hat=0.42 and sigma sub p-hat= square root of .42(.58)/1460= 0.013.

  2. p(p-hat ≥ .45)=.0099. About 10/1460 random samples of n=1460 will lead to 657 or more individuals (≥45%) w/ the characteristic.

  3. p(p-hat≤.4)=0.0606. Around 61/1460 random samples of n=1460 will lead to 584 or less people w/ the characteristic.

• 1. the sampling dis. of p hat is about normal with u sub p-hat=.39 and sigma sub p-hat= square root of .39(.61)=.022

  2. p(p-hat<.38)=.3233. About 32/100 random samples of n=500 adult americans will lead to fewer than 190 people (less than 38%) who believe marriage is obsolete.

  3. P(.40<p-hat.45)=.3203. About 32/100 random samples of n=500 adult americans will lead to 210 or more people (42% or more) who believe marriage is obsolete.

  4. p(p-hat≥.42)=.0845. ABout 8/100 random samples of n=500 adult americans will lead to 210+ individuals (42% or more) who think that marriage is obsolete. This is unusual.