The First National Bank of Wilson has 680 checking account customers. A recent sample of 60 of these customers showed 32 to have a Visa card with the bank.
Construct the 98 percent confidence interval for the proportion of checking account customers who have a Visa card with the bank. (Round your answers to 3 decimal places.)
Confidence interval for the proportion of checking account customers who have a Visa card with the bank is and .
To construct the confidence interval for the proportion of checking account customers who have a Visa card with the bank, we will use the formula for a confidence interval for a proportion.
The formula is:
Confidence Interval = sample proportion ± (critical value * standard error)
Step 1: Calculate the sample proportion
Since we know that 32 out of the 60 customers in the sample have a Visa card with the bank, the sample proportion is 32/60 = 0.533.
Step 2: Calculate the standard error
The standard error is calculated using the formula:
Standard Error = √((sample proportion * (1 - sample proportion))/sample size)
In this case, the sample size is 60 and the sample proportion (p) is 0.533.
Standard Error = √((0.533 * (1 - 0.533))/60) = 0.066
Step 3: Determine the critical value
To find the critical value, we need to determine the Z-score associated with a 98% confidence level. A Z-score table can be used to find this value.
A 98% confidence level corresponds to a critical value of Z = 2.33.
Step 4: Calculate the confidence interval
Now we can calculate the lower and upper bounds of the confidence interval using the formula:
Lower bound = sample proportion - (critical value * standard error)
Upper bound = sample proportion + (critical value * standard error)
Lower bound = 0.533 - (2.33 * 0.066) = 0.383
Upper bound = 0.533 + (2.33 * 0.066) = 0.683
Therefore, the 98 percent confidence interval for the proportion of checking account customers who have a Visa card with the bank is 0.383 and 0.683.