Estimating Sample Size

What is the formula for determining the sample size when estimating the population mean?

• n = (Z^2 * σ^2) / (E^2)

• n = (Z * σ) / (E^2)

• n = (Z^2 * σ) / (E)

• n = (Z * σ^2) / (E)

Discuss the impact of population standard deviation on the sample size calculation for estimating the population mean.

• A larger standard deviation requires a larger sample size

• A larger standard deviation requires a smaller sample size

• A larger standard deviation requires a smaller sample size

• Standard deviation has no impact on sample size calculation

How does the desired confidence level influence the sample size determination for estimating the population mean?

• It only affects the margin of error but not the level of significance

• It only affects the level of significance but not the margin of error

• It affects the margin of error and the level of significance in the calculation of the sample size.

• It has no impact on the sample size determination

Suppose a department store wants to estimate within 2 years the true mean age of the customers in its contemporary apparel department. The department store manager assumes a standard deviation of 7.5 years. How large a sample is required to estimate the true mean age with 95% confidence?

Round to the nearest whole number

• 56

• 112

• 420

• 224

A researcher wishes to estimate, within $25, the true mean amount of postage a community college spends each year. The standard deviation is known to be $80. If she wishes to be 95% confident in her estimate of the true mean amount of postage, how large a sample is necessary? Round to the nearest whole number

• 41

• 25

• 80

• 200

Discuss the factors that can affect the sample size calculation for estimating the population mean.

• Desired level of confidence, variability of the population, and margin of error

• Time of day the sample is collected

• Color of the population

• Number of people in the research team

Explain the concept of margin of error in the context of determining sample size for population mean estimation.

• The margin of error is the range of values within which the population mean is expected to fall.

• The margin of error is the level of confidence in the survey results.

• The margin of error represents the amount of random sampling error in a survey's results.

• The margin of error is the difference between the sample mean and the population mean.

A research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend exercising each week. They want to estimate the mean within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests that the standard deviation of the population is 2.2. Which of the following is the smallest sample size they could use?

• 60

• 75

• 90

• 180

• 120

• 61

• 69

• 105

• None of the other choices is correct

• 2

• 64

• 4

• 74

• None of the other choices is correct