Question

A random sample of 121 checking accounts at a bank showed an average daily balance of $280. The standard deviation of the population is known to be $66. Construct a 95% confidence interval estimates for the mean. (Round to two decimal places) [Answer , Answer ] Construct a 99% confidence interval for the mean. (Round to two decimal places) [Answer , Answer ]

Answer #1

We have given that,

Sample mean =$280

Population standard deviation=$66

Sample size=121

i) 95% confidence interval

Z critical value=1.96

Confidence interval formula is

Lower confidence limit =$268.24

Upper confidence limit =$291.76

ii) 99% confidence interval

Z critical value=2.58

Confidence interval formula is

Lower confidence limit =$264.52

Upper confidence limit =$295.48

Wachovia Bank has 800 checking account customers. A recent
sample of 60 of these showed 35 to have a Visa card with the
bank.
Construct the 99% confidence interval for the proportion of
checking account customers who have a Visa with the bank.
b. What sample size would be needed if you want the estimated
proportion to be within 4% of the population proportion at the 99%
confidence level?
if possible draw distributions?
Thanks in advance

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Confidence interval for the proportion is between and
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