Question

The ages of a group of 123 randomly selected adult females have a standard deviation of 16.2 years. Assume that the ages of female statistics students have less variation than ages of females in the general​ population, so let mean = 16.2 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics​ students? Assume that we want ​95% confidence that the sample mean is within​ a one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general​ population? The required sample size is ?

Answer 1

To estimate the mean age of all female statistics students with a 95% confidence level and a margin of error within half a year, we need to obtain a sample size of 163 female statistics student ages.

Step-by-step explanation:

To estimate the mean age of all female statistics students with a 95% confidence level and a margin of error within half a year, we need to calculate the required sample size. We can use the formula for sample size calculation:

n = (Z * σ / E)²

Where:

n = required sample size

Z = the Z-score associated with the desired confidence level, which is 1.96 for a 95% confidence level

σ = the standard deviation of the population, which is 16.2 years

E = the desired margin of error, which is 0.5 years

Plugging in the values:

n = (1.96 * 16.2 / 0.5)²

n ≈ 162.45

Since we cannot have a fraction of a student, we need to round up to the nearest whole number:

n = 163

Therefore, we need to obtain a sample size of 163 female statistics student ages in order to estimate the mean age of all female statistics students with a 95% confidence level and a margin of error within half a year.

Regarding whether it is reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population, it depends on the specific context and underlying reasons for the assumption.