Estimating a Population Mean

Do high school seniors with part-time jobs spend less time doing homework per week, on average, than seniors without part-time jobs? For a random sample of 45 seniors with part-time jobs, the mean amount of homework time is 4.2 hours with a standard deviation of 3.8 hours. For a random sample of 45 seniors without part time jobs, the mean amount of homework time is 5.8 hours with a standard deviation of 4.9 hours. Assuming the conditions are met, which of the following is the correct margin of error for a 95% confidence interval for a difference in the population means?

• 0.924

• 1.989

• 1.838

• -1.6

• 82.867

Answer explanation

Be careful to not confuse the means with the standard deviations in this expression.

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)

What is the significance level and how does it affect the sample size calculation for estimating the population mean?

• It determines the color of the confidence interval

• It has no effect on the sample size calculation

• It is used to calculate the median instead of the mean

• It affects the sample size calculation by determining the critical value for the confidence interval.

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

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

What are the different methods available for determining the sample size for estimating the population mean?

• Asking friends and family

• Using a magic eight ball

• Guessing randomly

• Using a formula, using a sample size calculator, consulting statistical experts

Provide an example of determining the sample size for estimating the population mean using a specific formula or method.

• n = (Z^2 * σ) / (E)

• n = (Z * σ) / (E)

• n = (Z^2 * σ^2) * E

• Using the formula n = (Z^2 * σ^2) / (E^2)

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.

• $1536.50 - $1603.50

• $1568.50 - $1571.50

• $1568.70 - $1595.60

• $1548.60 - $1591.40