In: Statistics and Probability
The First National Bank of Wilson has 740 checking account customers. A recent sample of 60 of these customers showed 36 have a Visa card with the bank.
Construct the 98% 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 . |
Solution :
Given that,
n = 60
x = 36
= x / n = 36 / 60 = 0.600
1 - = 1 - 0.600 = 0.400
At 98% confidence level the z is ,
= 1 - 98% = 1 - 0.98 = 0.02
/ 2 = 0.02 / 2 = 0.01
Z/2 = Z0.01 = 2.326
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.326 (((0.600 * 0.400) / 60)
= 0.147
A 98% confidence interval for population proportion p is ,
- E < P < + E
0.600 - 0.147 < p < 0.600 + 0.147
0.453 < p < 0.747
Confidence interval for the proportion is between 0.453 and 0.747 .