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STA 2381 Cumulative Exam |Questions with Correct Verified Answers
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STA 2381 Cumulative Exam |Questionswith Correct Verified Answers
T/F: The width of a confidence interval decreases as the sample size increases for a fixed
confidence interval, provided the sample standard deviation remains constant - ANSWER True
(as sample size increases, CI decreases.
As sample size decreased, CI increases)
T/F: Confidence intervals give no information regarding the precision of an estimator - ANSWER
False
precision of an estimator is measured through confidence intervals
T/F: The width of a confidence interval for the population mean depends only on the
parameter value it is attempting to estimate - ANSWER confidence interval only depends on
-t-value
-(sample standard deviation=sample standard error)
doesn't depend on parameter at all
(if we knew the parameter, we wouldn't have to calculate the confidence interval at all)
What shape is the population density function? - ANSWER The density function can be any
shape as long as it isn't negative
Random sampling - ANSWER every element in the population is equally likely to be sampled
,Are random samples and representative samples the same thing? - ANSWER NO.
Parameter - ANSWER a descriptive measure for a population
Statistic - ANSWER a descriptive measure for a sample
T/F: A disadvantage of using a 99 percent confidence level rather than a 95 percent confidence
interval is that larger samples must be taken for establishing higher levels of confidence -
ANSWER False
It doesn't have to do with sample sizes.
The disadvantage with larger percentages is that the interval is wider, which doesn't
actually help in determining precision.
Does the sample mean equal the population mean? - ANSWER No. However, the mean of the
sampling distribution of X(bar) is equal to the population mean
For continuous random variables, the probability of getting any one value equals: - ANSWER 0
Population standard deviation (sigma) is an example of what type of parameter? - ANSWER
dispersion parameter
For what type of random variables does Chevbyshev's theorem apply? - ANSWER For
ALL random variables
For what type of random variables does the Empirical rule theorem apply? - ANSWER For
random variables that are symmetric and unimodal
Population variance - ANSWER (sigma)2
,(aka standard deviation squared)
Sample variance - ANSWER s2
(T/F) sample variance is an estimator of population variance - ANSWER true
How many normal random variables are there? - ANSWER Infinitely many
Can standard deviation be negative? - ANSWER No
What random variables have a probability distribution? - ANSWER ALL random variables have a
probability distribution called the sampling distribution as along as what we have is a simple
random sample
(T/F) The sampling error is a mistake made in the sampling - ANSWER False. The sampling
error is just the difference between the statistic and the parameter. It says the statistic isn't
exactly the parameter
How is X(bar) related to mu? - ANSWER X(bar) is an estimator of mu
The area under the population density function integrates to: - ANSWER 1
MUST
T/F: Any function of the sample data is an estimator - ANSWER False
any function of the sample data is a STATISTIC
T/F: Every estimator is a statistic, but not every statistic is an estimator - ANSWER True
, T/F: Every estimator of a population parameter is a random variable which has its own
density function - ANSWER True
T/F: Every estimator is a statistic - ANSWER True
Every estimator is a statistic and a random variable
T//F: Statistics are any function of the sample data - ANSWER True
T/F: Statistical inference occurs when population parameters are used to infer the values
of statistics - ANSWER False
Statistical inference occurs when SAMPLE DATA is used to infer the values of statistics
T/F: Every random sample is a representative sample - ANSWER False
T/F: Parameters describe characteristics of the population of interest - ANSWER True
T/F: The population mean mu is an example of an estimator - ANSWER
False mu is a parameter
x bar is an estimator of the parameter
The central limit theorem plays a key role in developing a confidence interval for the population
mean. - ANSWER True
T/F: The terms random variable and population of interest are often interchanged in statistical
analysis - ANSWER True
T/F: The population mean, population median, and population mode are the same value -
ANSWER False
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