7.3. CONFIDENCE INTERVAL FORP 95 Math 150 Name: Homework 7.3 Date: 1.- A recent

Question

7.3. CONFIDENCE INTERVAL FORP 95 Math 150 Name: Homework 7.3 Date: 1.- A recent study involving 200 people in Los Angeles found that 123 are religious. (a) Find a 95% confidence interval for the true proportion of individuals in Los Angeles that are religious. (b) What is the sarnple size needed in order to have a margin of error of 1%? 2.- A survey of 300 college students found that 200 believe in the existence of Santa Claus. (a) Find a 99% confidence interval for the population proportion of college students that believe in Santa Claus. (b) what is the sample size needed in order to have a margin of error of 3%?

Explanation / Answer

Q-1

Part-a

95% CI= 123/200±1.96*sqrt((123/200)*(1-123/200)/200)=( 0.5476            0.6824)

Part-b

Sample size n>p*(1-p)*(z/E)2=((123/200)*(1-123/200))*(1.96/0.01)2=9095.9484

So, sample size n=9096

Q-2

Part-a

99% CI= 200/300±2.58 *sqrt((200/300)*(1-200/300)/300)=( 0.596447961                0.736885373)

Part-b

Sample size n>p*(1-p)*(z/E)2=((200/200)*(1-200/300))*(2.58/0.03)2=2465.33

So, sample size n=2466

Q-3

Part-a

90% CI= 0.45±1.645 *sqrt(0.45*(1-0.45)/250)=( 0.3982    0.5018)

Part-b

99% CI= 0.45±2.58 *sqrt(0.45*(1-0.45)/250)=( 0.3688      0.5312)

Part-c

99% CI is wider because it needs more confidence.

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