Question

Now the World Bank wants to examine the proportion of Tanzanian women who have access to a financial account. To do so, statisticians take a simple random sample of 600 Tanzanian women, out of a population of about 29 million and find that 43.5 percent of the sample have access to a financial account.

1. Calculate a 95 percent confidence interval for this proportion.
2. Calculate a 99 percent confidence interval for this proportion.

Answer 1

Answer:

sample size: n= 600

sample proportion:

a)

Confidence level: c = 95%

formula for confidence inteval is

where Zc is the z critical value for c= 95%

Zc= 1.96

0.39533 < P < 0.47467

rounding to 3 decimals

0.395 < P < 0.475

Thus we get 95% confidence interval as ( 0.395 ,  0.475)

b)

Confidence level: c = 99%

formula for confidence inteval is

where Zc is the z critical value for c= 99%

Zc= 2.576

0.38287 < P < 0.48713

rounding to 3 decimals

0.383 < P < 0.487

Thus we get 99% confidence interval as ( 0.383 ,  0.487 )