Answer to Question #219922 in Statistics and Probability for sai

Question #219922

According to a​ newspaper, 59​% of high school seniors have a​ driver's license. Suppose we take a random sample of 100 high school seniors and find the proportion who have a​ driver's license.

a. What value should we expect for our sample​ proportion?

b. What is the standard​ error?

c. Use your answers to parts​ (a) and​ (b) to complete this​ sentence:

We expect​ ____% to have their​ driver's license, give or take​ _____%.

d. Suppose we increased the sample size from 100 to 300. What effect would this have on the standard​ error? Recalculate the standard error to see if your prediction was correct.



1
Expert's answer
2021-07-27T05:51:27-0400

a.

E(pˉ)=p=0.59E(\bar{p})=p=0.59

b.


se(pˉ)=p(1p)n=0.59(10.59)1000.0492se(\bar{p})=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.59(1-0.59)}{100}}\approx0.0492



c. We expect​ 5959 % to have their​ driver's license, give or take 4.924.92 %.


d. If we increased the sample size from 100 to 300, then the standard error will decrease by a factor of 3\sqrt{3} .


E(pˉ)=p=0.59E(\bar{p})=p=0.59

se(pˉ)=p(1p)n=0.59(10.59)3000.0284se(\bar{p})=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.59(1-0.59)}{300}}\approx0.0284

We expect​ 5959 % to have their​ driver's license, give or take 2.842.84 %.




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