Confidence interval

What is the formula for calculating a confidence interval for the mean of a normal distribution when the population variance is known?

• (x̄ - zα/2σ/√n, x̄ + zα/2σ/√n)

• (x̄ - tα/2σ/√n, x̄ + tα/2σ/√n)

• (x̄ - zα/2s/√n, x̄ + zα/2s/√n)

• (x̄ - tα/2s/√n, x̄ + tα/2s/√n)

What is the relationship between the confidence level and the width of a confidence interval?

• As the confidence level increases, the width of the interval decreases.

• As the confidence level decreases, the width of the interval decreases.

• As the confidence level increases, the width of the interval increases.

• As the confidence level decreases, the width of the interval increases.

A random sample of 50 observations is drawn from a normally distributed population with a known variance of 25. The sample mean is 75. What is the 95% confidence interval for the population mean?

• (72.59, 77.41)

• (73.64, 76.36)

• (74.27, 75.73)

• (74.53, 75.47)

A confidence interval is calculated for the mean of a normal distribution with a known variance using a sample of size n. How does increasing the sample size affect the width of the interval?

• Increasing the sample size will always decrease the width of the interval.

• Increasing the sample size will always increase the width of the interval.

• Increasing the sample size may increase or decrease the width of the interval, depending on the sample mean and population variance.

• Increasing the sample size has no effect on the width of the interval.

The margin of error for a confidence interval is affected by which of the following factors?

• Sample size and confidence level

• Sample size and population size

• Population size and confidence level

• Population size and population variance

What is the formula for the t-statistic when calculating a confidence interval for the mean of a normal distribution with an unknown population variance, using a sample of size n?

• (x̄ - μ)/(σ/√n)

• (x̄ - μ)/(s/√n)

• (x̄ - μ)/(s/√n) *√(n-1)

• (x̄ - μ)/(σ/√n) *√(n-1)

A confidence interval is calculated for the mean of a normal distribution with an unknown variance using a sample of size n. How does increasing the sample size affect the width of the interval, assuming all other factors remain constant?

• Increasing the sample size may increase or decrease the width of the interval, depending on the sample mean and standard deviation.

• Increasing the sample size will always increase the width of the interval.

• Increasing the sample size will always decrease the width of the interval.

• Increasing the sample size has no effect on the width of the interval.

A random sample of 500 individuals is taken from a population. 250 of them have a certain characteristic. What is the 95% confidence interval for the true population proportion?

• (0.45, 0.54)

• (0.49, 0.51)

• (0.50, 0.52)

• (0.51, 0.53)

When constructing a confidence interval for population proportion using a large sample, which of the following is used to estimate the standard error?

• The sample size

• The sample proportion

• The population size

• The population proportion

A confidence interval is calculated for the population proportion using a large sample. How does increasing the sample size affect the width of the interval, assuming all other factors remain constant?

• Increasing the sample size has no effect on the width of the interval.

• Increasing the sample size will always increase the width of the interval.

• Increasing the sample size may increase or decrease the width of the interval, depending on the sample proportion.

• Increasing the sample size will always decrease the width of the interval.