Confidence Interval with Means Review

What does it mean for a distribution to be skewed?

• A skewed distribution is one where the data points are symmetrically distributed around the mean.

• A skewed distribution is one where the data points are evenly spread across the range.

• A skewed distribution is one where the data points are not symmetrically distributed around the mean, leading to a longer tail on one side of the distribution.

• A skewed distribution is one where the data points cluster around the median.

What is the role of the z-score in confidence intervals?

• It indicates the sample size required for the study.

• It represents the number of standard deviations a data point is from the mean and is used to determine the width of the confidence interval based on the desired confidence level.

• It is used to calculate the mean of the data set.

• It determines the significance level of the hypothesis test.

What is the impact of a skewed population on the sampling distribution of the sample mean?

• A skewed population may require a larger sample size for the sampling distribution of the sample mean to approximate normality.

• A skewed population has no effect on the sampling distribution of the sample mean.

• A skewed population will always result in a normal sampling distribution regardless of sample size.

• A skewed population will lead to a smaller standard error of the mean.

What does it mean if a value is not included in a confidence interval?

• It indicates that the value is a plausible estimate of the population parameter.

• It suggests that this value is not a plausible estimate of the population parameter based on the sample data.

• It means that the sample size is too small to make any conclusions.

• It implies that the confidence interval was calculated incorrectly.

What is the formula for calculating a confidence interval for a mean?

• CI = x̄ ± z*(σ/√n)

• CI = x̄ ± t*(σ/√n)

• CI = x̄ ± z*(n/σ)

• CI = x̄ ± (σ/n)

How do you interpret a confidence interval of (1.80, 3.85) hours?

• This interval suggests that we are confident that the true mean time managers spend on paperwork lies between 1.80 and 3.85 hours.

• The interval indicates that 1.80 hours is the maximum time spent on paperwork.

• The confidence interval shows that the average time spent on paperwork is exactly 2.83 hours.

• This interval means that there is a 95% chance that the time spent on paperwork is between 1.80 and 3.85 hours.

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

• As the confidence level increases, the width of the confidence interval decreases, meaning we are more certain and more precise.

• As the confidence level increases, the width of the confidence interval remains the same, indicating a constant level of certainty and precision.

• As the confidence level increases, the width of the confidence interval also increases, meaning we are more certain but less precise.

• As the confidence level decreases, the width of the confidence interval increases, indicating less certainty and more precision.

What is a confidence interval?

• A method to calculate the mean of a data set.

• A range of values likely to contain an unknown population parameter.

• A statistical test to determine the significance of results.

• A graphical representation of data distribution.

What is the difference between a sample mean and a population mean?

• The sample mean is the average of a sample taken from a population, while the population mean is the average of all possible values in the entire population.

• The sample mean is always larger than the population mean.

• The sample mean is calculated using the entire population, while the population mean is calculated using a sample.

• The sample mean and population mean are always equal.

What does it mean to be 99% confident in a confidence interval?

• It means that 99% of the time, the sample mean will be equal to the population mean.

• It indicates that if we take many samples, 99% of those confidence intervals will contain the true population mean.

• It suggests that there is a 99% chance that the population mean lies within the interval for any single sample.

• It means that the confidence interval will be accurate 99% of the time for any given sample.