Final answer:
A minimum sample size of 64 business students must be randomly selected to estimate the mean monthly earnings with 95% confidence within $140 of the true population mean, given the population standard deviation of $569.
Step-by-step explanation:
To find the minimum sample size required to estimate an unknown population mean μ with a certain level of confidence, we can use the formula:
n = (Z*σ/E)^2
Where:
- n is the sample size
- Z is the Z-score corresponding to the desired confidence level
- σ (sigma) is the population standard deviation
- E is the margin of error
For a 95% confidence level, the Z-score is approximately 1.96. The population standard deviation σ is given as $569. The margin of error E is $140.
Plugging these values into the formula, we get:
n = (1.96*569/140)^2
n = (1114.44/140)^2
n = (7.96)^2
n = 63.4
Since the sample size must be a whole number, we would round up to the next whole number which gives us a minimum sample size of 64 business students that must be randomly selected to estimate the mean monthly earnings of business students at one college with the desired precision and confidence level.