Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. Given the information in the Microsoft Excel Online file below, construct a spreadsheet to determine how large a sample should be taken for each desired margin of error.
For a margin of error of ± $300, the required sample size is n =
I tried 600 but it is wrong
To determine the required sample size for a desired margin of error, you can use the formula:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-value for the desired level of confidence (in this case, 95% confidence corresponds to a Z-value of approximately 1.96)
σ = standard deviation (in this case, unknown)
E = margin of error (in this case, ±$300)
Since the standard deviation (σ) is unknown, you need to estimate it using the range method. The range is the difference between the highest and lowest values in the sample.
To calculate the sample size, follow these steps:
1. Calculate the range of the given data:
- In Excel, select a cell and use the formula "=MAX(B2:B15)-MIN(B2:B15)" (assuming the starting salaries data is in column B, from B2 to B15).
2. Estimate the standard deviation (σ) using the range:
- In a new cell, use the formula "=B16/4" (assuming the range is in cell B16 and dividing it by 4 gives a conservative estimate of the standard deviation).
3. Calculate the sample size (n):
- In another cell, use the formula "=((1.96*B17)/300)^2" (assuming the estimated standard deviation is in cell B17 and the margin of error is $300).
The resulting value will be the required sample size (n). Round it up to the nearest whole number since the sample size must be an integer.
Make sure you adjust the cell references and formulas according to your specific Excel file layout.