. An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within one year of the population mean. Assume the population of ages is normally distributed. Determine the minimum required sample size to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.2 years
If you want an expert to help you, you'll type the name of your subject in the school subject box.
580
To determine the minimum required sample size to construct a 90% confidence interval for the population mean, we can use the formula:
n = (Z * σ / E)^2
where:
- n is the required sample size
- Z is the z-score corresponding to the desired confidence level (90% confidence corresponds to a z-score of approximately 1.645)
- σ is the population standard deviation
- E is the maximum margin of error (in this case, 1 year)
Plugging in the given values, we can calculate the minimum required sample size:
n = (1.645 * 1.2 / 1)^2
n = 1.974^2
n ≈ 3.896
So, the minimum required sample size to construct a 90% confidence interval for the population mean is approximately 4.
To determine the minimum required sample size to construct a 90% confidence interval for the population mean, we need to use the following formula:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (in this case, 90% confidence level)
σ = population standard deviation
E = maximum error margin or maximum difference between the sample mean and the population mean
In this case, we want the maximum difference or error margin to be 1 year, and the population standard deviation is given as 1.2 years. The Z-score for a 90% confidence level is approximately 1.645.
Plugging these values into the formula:
n = (1.645 * 1.2 / 1)^2
n = 4.6746
Since we cannot have a fraction of a student, we round up the sample size to the nearest whole number:
n = 5
Therefore, the minimum required sample size to construct a 90% confidence interval for the population mean is 5 students.