Statistics Chapters 7-
8(STA 2023) Exam
Questions and Complete
Solutions Graded A+
Point Estimate - Answer: Is a specific value estimate of a parameter.
Estimator - Answer: A statistic used to estimate a parameter
Unbiased Estimator - Answer: An estimator whose value approximates the expected value of a
population parameter, used for the variance or standard deviation when the sample size is less than 30;
an estimator whose expected value or mean must be equal to the mean of the parameter being
estimated
Consistent Estimator - Answer: An estimator whose value approaches the value of the parameter
estimated as the sample size increases
Relatively Efficient Estimator - Answer: An estimator that has the smallest variance of all the statistics
that can be used to estimate a parameter
Interval Estimate - Answer: A range of values used to estimate a parameter
The interval must be larger if you want to be 99 or 99.5 confident
Confidence Level - Answer: The probability that a parameter lies within the specified interval estimate of
the parameter
, Confidence Interval - Answer: Is a specific interval estimate of a parameter determined by using data
obtained from a sample and by using the specific confidence level of the estimate
Margin of Error(Maximum Error of the Estimate - Answer: The maximum likely between the point
estimate of a parameter and the actual value of the parameter
Raw Data - Answer: Data collected in original form
T-Distribution - Answer: A family of bell-shaped curves based on degrees of freedom, similar to the
standard normal distribution with the exception that the variance is greater than 1; used when you are
testing small samples and when the population standard deviation is unknown
Characteristics of the T-Distribution - Answer: 1. It is bell-shaped
2. It is symmetric about the mean
3. The mean, median and mode are equal to 0 and are located at the center of the distribution.
4. The curve approaches but never touches the x-axis
5. The variance is greater than 1
6. The t distribution is actually a family of curves based on the concept of degree of freedom, which is
related to sample size.
Degrees of Freedom - Answer: The number of values that are free to vary after a sample statistic has
been computed; used when a distribution(such as the t distribution) consists of a family of curves
Ex: if the mean of 5 values is 10, then 4 of the 5 values are free to vary. But once 4 values are selected,
the fifth value must be a specific number to get a sum of 50, since 50/5=10
Proportion - Answer: A part of a whole, represented by a freaction, a decimal, or a percentage
p hat - Answer: sample proportion
q hat - Answer: 1 - p hat
8(STA 2023) Exam
Questions and Complete
Solutions Graded A+
Point Estimate - Answer: Is a specific value estimate of a parameter.
Estimator - Answer: A statistic used to estimate a parameter
Unbiased Estimator - Answer: An estimator whose value approximates the expected value of a
population parameter, used for the variance or standard deviation when the sample size is less than 30;
an estimator whose expected value or mean must be equal to the mean of the parameter being
estimated
Consistent Estimator - Answer: An estimator whose value approaches the value of the parameter
estimated as the sample size increases
Relatively Efficient Estimator - Answer: An estimator that has the smallest variance of all the statistics
that can be used to estimate a parameter
Interval Estimate - Answer: A range of values used to estimate a parameter
The interval must be larger if you want to be 99 or 99.5 confident
Confidence Level - Answer: The probability that a parameter lies within the specified interval estimate of
the parameter
, Confidence Interval - Answer: Is a specific interval estimate of a parameter determined by using data
obtained from a sample and by using the specific confidence level of the estimate
Margin of Error(Maximum Error of the Estimate - Answer: The maximum likely between the point
estimate of a parameter and the actual value of the parameter
Raw Data - Answer: Data collected in original form
T-Distribution - Answer: A family of bell-shaped curves based on degrees of freedom, similar to the
standard normal distribution with the exception that the variance is greater than 1; used when you are
testing small samples and when the population standard deviation is unknown
Characteristics of the T-Distribution - Answer: 1. It is bell-shaped
2. It is symmetric about the mean
3. The mean, median and mode are equal to 0 and are located at the center of the distribution.
4. The curve approaches but never touches the x-axis
5. The variance is greater than 1
6. The t distribution is actually a family of curves based on the concept of degree of freedom, which is
related to sample size.
Degrees of Freedom - Answer: The number of values that are free to vary after a sample statistic has
been computed; used when a distribution(such as the t distribution) consists of a family of curves
Ex: if the mean of 5 values is 10, then 4 of the 5 values are free to vary. But once 4 values are selected,
the fifth value must be a specific number to get a sum of 50, since 50/5=10
Proportion - Answer: A part of a whole, represented by a freaction, a decimal, or a percentage
p hat - Answer: sample proportion
q hat - Answer: 1 - p hat
