Point Estimates+ Basics
What branch of statistics involves the process of estimating the value of a parameter from information obtained from a sample?
What is inferential statistics
What is the formula for a 100(1 - α)% Confidence Interval for a population mean μ when σ is known?
What is x±Zα/2*σ/√n
What is the formula used to find the minimum sample size (n) needed for an interval estimate of the population mean?
What is n≥((Zα/2⋅σ)/E)^2
What sample statistic is used to estimate σσ when the population standard deviation is unknown?
What is The sample standard deviation, s.
How is the sample proportion (p) calculated mathematically using observations?
What is p=number of observations that have a characteristic of interest / total number of observations in a sample
This term refers to a specific numerical value estimate of a parameter, where the best estimate of the population mean (μ) is the sample mean (x).
What is a point estimate
What are the three most common confidence levels used in statistics?
What is 90%, 95%, and 99%.
In sample size determination for a mean, if a sociologist wants to estimate automobile thefts within 2 automobiles (E=2) with 99% confidence and a standard deviation of 4.2, what formula component does the number 2 represent?
What is The margin of error (E)
When σ is unknown and sample sizes are small (n<30), critical values are taken from this distribution instead of the standard normal z-distribution.
What is The t-distribution
If p represents the sample proportion, how is q calculated?
This property of a good estimator means that the expected value or mean of the estimates obtained from samples of a given size is equal to the parameter being estimated (E(X)=μ).
What is an unbiased estimator
This term describes the maximum likely difference between the point estimate of a parameter and the actual value of the parameter (also called the maximum error of the estimate).
What is The margin of error (or error bound, E).
True or False: Sample size determination is closely related to statistical estimation and its formula is derived directly from the margin of error formula.
What is true
How are the degrees of freedom (df) calculated for a specific confidence interval when using the t-distribution for a single mean?
What is df=n−1 (where n is the sample size).
What two criteria/conditions must be met regarding np and nq before constructing a confidence interval about a proportion?
What is np≥5 and nq≥5
This property means that as the sample size increases, the value of the estimator approaches the true value of the parameter being estimated.
What is a consistent estimator
What two main assumptions must be met regarding the sample and population distribution to find a confidence interval for a mean when σ is known?
What is The sample is a random sample
- And the population distribution is normal, or the sample size is larger than 30 (n>30) to use the Central Limit Theorem (CLT).
If the variance of a water temperature dataset is 28°F, what value must you calculate or extract before plugging it into the sample size formula for the mean?
What is The standard deviation (σ), which is the square root of the variance (√28)
What happens to the t-distribution curve as the sample size (n) increases?
What is It approaches the standard normal distribution.
What value should you use for p if no prior approximation or estimate of p is known when determining minimum sample size for a proportion?
What is p=0.5
(which gives a sample size sufficiently large to guarantee an accurate prediction).
Of all the statistics that can be used to estimate a parameter, this type of estimator has the smallest variance.
What is a relatively efficient estimator
What does it mean if a statistical technique is described as "robust"?
What is The distribution of the variable can depart somewhat from normality, and valid conclusions can still be obtained.
When calculating sample size, what should you always do to your final calculated value of nn if it results in a decimal number (for example, n=41.1)?
What is Always round up to the next whole number (e.g., n≥42) to guarantee the required accuracy and confidence level.
Name two properties that the t-distribution shares with the standard normal distribution, and one way it differs.
What is Shared: Bell-shaped, symmetric about the mean, mean/median/mode equal zero at the center, approaches but never touches the x-axis.
What is Differs: Variance is greater than 1, and it is a family of curves based on degrees of freedom.
What is the formula to find the minimum sample size (n) needed for an interval estimate of a population proportion?
What is n≥p⋅q⋅(Zα/2)^2/E^2