The First National Bank of Wilson has 700 checking account customers. A recent s

Question

The First National Bank of Wilson has 700 checking account customers. A recent sample of 70 of these customers showed 26 have a Visa card with the bank.

Construct the 95% confidence interval for the proportion of checking account customers who have a Visa card with the bank. (Use z Distribution Table.) (Round your answers to 3 decimal places.)

Confidence interval for the proportion is between  and .

The First National Bank of Wilson has 700 checking account customers. A recent sample of 70 of these customers showed 26 have a Visa card with the bank.

Explanation / Answer

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=26
Sample Size(n)=70
Sample proportion = x/n =0.371
Confidence Interval = [ 0.371 ±Z a/2 ( Sqrt ( 0.371*0.629) /70)]
= [ 0.371 - 1.96* Sqrt(0.003) , 0.371 + 1.96* Sqrt(0.003) ]
= [ 0.258,0.484]
Interpretations:
1) We are 95% sure that the interval [0.258 , 0.484 ] contains the true population proportion
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion  

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