A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 20 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of 235.29. Assume the data is normally distributed. Find a 98% confidence interval for the true mean checking account balance for local customers. State the following:

Critical t/z score (which one?): ___________ value __________

Margin of error: E=_______(nearest cent)

Write the confidence interval as indicated below, rounding values to the nearest cent.
Confidence Interval:_________<μ<_____________

To find the 98% confidence interval for the true mean checking account balance for local customers, we can use the t-distribution since the sample size is less than 30.

Step 1: Determine the critical t-score.
Since the sample size is 20, and we want a 98% confidence interval, we need to find the critical t-score with 19 degrees of freedom. We can find this value using a t-table or a statistical software. For a 98% confidence level with 19 degrees of freedom, the critical t-score is approximately 2.860.

Critical t-score: 2.860

Step 2: Calculate the margin of error.
The margin of error is given by the formula:
Margin of error (E) = t-score * standard deviation / square root of the sample size

In this case, the t-score is 2.860, the standard deviation is 235.29, and the sample size is 20.
E = 2.860 * 235.29 / sqrt(20)
E ≈ 120.71 (nearest cent)

Margin of error: E ≈ $120.71

Step 3: Calculate the confidence interval.
The confidence interval can be calculated using the formula:
Confidence Interval = Sample mean ± Margin of error

In this case, the sample mean is $664.14 and the margin of error is $120.71.
Lower limit = Sample mean - Margin of error = $664.14 - $120.71 = $543.43
Upper limit = Sample mean + Margin of error = $664.14 + $120.71 = $784.85

Confidence Interval: $543.43 < μ < $784.85

So, the required information is:

Critical t-score: 2.860 (rounded to 3 decimal places)
Margin of error (E): $120.71 (nearest cent)
Confidence Interval: $543.43 < μ < $784.85