A large bank believes that one-third of its checking customers have used at least one of the bank's other services during the past year. How large a sample is required to estimate the actual proportion within a range of plus and minus 0.04? Use the 98 percent level of confidence.

Try this formula:

n = [(z-value)^2 * p * q]/E^2
...where n = sample size needed; z-value is found using a z-table; p = 1/3; q = 2/3; E = .04

Determine the z used for 98% confidence by checking a z-table. Convert all fractions to decimals. Plug values into the formula to determine n. Round answer to the next highest whole number.

I hope this will help get you started.

Well, let me see if I got this straight. The bank wants to estimate the proportion of checking customers who have used other bank services within a certain range, right?

To determine the sample size needed, we'll have to consider a few factors. First, the desired range is plus or minus 0.04, which means we want an estimate that is accurate within that range. Additionally, we want a 98 percent level of confidence, which means we want to be pretty darn sure about our estimate.

Now, since we're dealing with proportions, we can use the formula for sample size estimation for proportions. The formula is: n = (Z^2 * p * (1 - p)) / (E^2)

In this formula, n represents the desired sample size, Z is the Z-score corresponding to the desired level of confidence (in this case, 2.33 for a 98 percent confidence level), p is the estimated proportion of customers (in this case, 1/3 or approximately 0.3333), and E is the desired margin of error (in this case, 0.04 or 0.04 * 100% = 4%).

Plugging in the values, we get:
n = (2.33^2 * 0.3333 * (1 - 0.3333)) / (0.04^2)

Crunching the numbers, we find that the bank would need a sample size of approximately 2260 customers to estimate the proportion within a range of plus or minus 0.04, with a 98 percent level of confidence.

So, you better prepare a big clown car to accommodate all those customers, or maybe just tell the bank to settle for fewer clowns, I mean, customers in their sample.

To determine the sample size required to estimate the actual proportion within a range of plus and minus 0.04 with a 98 percent level of confidence, we can use the formula:

n = ((Z * σ) / E)^2

Where:
n = sample size
Z = Z-score corresponding to the desired level of confidence (in this case, 98 percent)
σ = standard deviation or estimated proportion (in this case, since no information about the standard deviation is given, we will use 0.5 as a conservative estimate since it produces the largest required sample size)
E = margin of error (in this case, 0.04)

Since we are interested in estimating the proportion of checking customers who have used at least one other service, we will use the estimated proportion of one-third, which can be expressed as 0.33.

Now, let's calculate the required sample size:

n = ((Z * σ) / E)^2
n = ((2.33 * 0.33 * (1 - 0.33)) / 0.04)^2
n = ((2.33 * 0.33 * 0.67) / 0.04)^2
n = (0.5415 / 0.04)^2
n = 13.5375^2
n ≈ 183.5506

Therefore, a sample size of approximately 184 is required to estimate the actual proportion within a range of plus and minus 0.04 with a 98 percent level of confidence.

To determine the sample size required to estimate the actual proportion within a given range with a specific level of confidence, we can use the formula for the sample size for proportions:

n = (Z^2 * p * (1 - p)) / E^2

Where:
- n is the required sample size
- Z is the z-score corresponding to the desired level of confidence
- p is the estimated proportion (0.33 in this case)
- E is the desired margin of error (0.04 in this case)

First, we need to find the z-score for the 98% confidence level. The z-score can be obtained using a standard normal distribution table or a calculator. For a 98% confidence level, the corresponding z-score is approximately 2.33.

Substituting the given values into the formula, we have:

n = (2.33^2 * 0.33 * (1 - 0.33)) / 0.04^2

n = (5.4289 * 0.33 * 0.67) / 0.0016

n ≈ 3.3927 / 0.0016

n ≈ 2120.44

Therefore, a sample size of approximately 2121 is required to estimate the actual proportion within a range of plus and minus 0.04 at a 98% confidence level.