5) 98% confidence; the sample size is 800, of which 40% are successes 6) In a ra

ID: 3227955 • Letter: 5

Question

5) 98% confidence; the sample size is 800, of which 40% are successes 6) In a random sample of 192 college students, 129 had part-time jobs. Find the margin of error for the 95% confidence interval used to estimate the population proportion Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p Use the given data to find the minimum sample size required to estimate the Population proportion equiv 8) Margin of error: 0.04; confidence 95% or study, p is estimated the pri valent of 60%. solve the problem. Round the point estimate to the thousandth. they rented obtain a 9) 32 randomly picked people were asked if nearest own home, 8 said they rented or owned their point estimate of the proportion of home owners. A-2

Explanation / Answer

Solution :-

5. Question: 98% confidence; the sample size is 800, of which 40% are successes.

Answer: sample size = n = 800.
z_c = 2.054 at 98% confidence
p = 40% = 0.40
standard error = s.e. = [p(1-p)/n] = 0.0173
margin of error = E = s.e.× z_c = 0.0173 × 2.054 = 0.0356
98% confidence interval for this proportion = ( 0.40 - 0.0356, 0.40 + 0.0356 ) = ( 0.3644, 0.4356 )
98% confidence interval for this percentage of successes is (36%, 44%)

6. Question: in a random sample of 192 college student 129 had part time jobs. find the margin of error for the 95 percent confidence interval used to estimate the population proportion.

Answer: Out of 192 college students 129 have part time jobs.
Hence the given sample proportion is p = 129/192 = 0.672

The estimated population proportion is p* = 0.672
Standard error = sqrt[p*(1 - p*)/n] = 0.034
Now, z*-Value for 95% confidence interval is 1.96
Hence margin of error is 1.96 x 0.034 = 0.067

7. Question: n = 56 x = 30 95 confidence

Answer: Confidence interval for population proportion is
sample proportion +/- margin of error
Margin of error = Confidence coefficient * Standard error of p
Sample proportion = p = x/n = 30/56 = 0.536
Confidence coefficient is the critical value of z for 95% confidence = 1.96
Standard error of p = sqrt [p*(1-p)/n]
The CI is
0.536 +/- 1.96*sqrt [0.54*0.46/56]
0.536 +/- 0.131

0.405<p<0.667

8. Question:

Margin of error: 0.04; confidence level: 95%; from a prior study, p is estimated by the decimal
equivalent of 60%.

Answer:

p = 0.6
z = 1.96 (use a table or calculator)
E = 0.04

n = p(1-p)(z/E)^2

n = 0.6(1-0.6)(1.96/0.04)^2
n = 576.24
n = 577 ... Round up to the nearest whole number
The min sample size required is 577

9. Question: 32 randomly picked people were asked if they rented or owned their own home, 8 said they rented. Obtain a point estimate of the proportion of home owners.

Answer: n = 32,

Rented = 8

Owners = 24

Point estimate of the proportion of home owners = 24/32 = 0.750