MGSC 291 EXAM 2 QUESTIONS & ANSWERS
A consistent estimator for the mean: - Answers -converges on the true parameter μ as
the sample size increases.
pi - Answers -is the proportion successes in a binomial distribution
important properties of estimators - Answers -unbiased
efficient
consistent
Central Limit Theorem - Answers -The theory that, as sample size increases, the
distribution of sample means of size n, randomly selected, approaches a normal
distribution.
np>10
n(1-p)>10
Z score for confidence interval - Answers -1.645 1.96 2.576
Type 1 error - Answers -Rejecting null hypothesis when it is true
type 2 error - Answers -failing to reject a false null hypothesis
Twenty randomly selected statistics students were given 15 multiple choice questions
and 15 open-ended questions, all on the same material. The professor was interested in
determining if students scored higher on the multiple choice questions. This experiment
is an example of _______. - Answers -A paired t-test
sampling variation - Answers -the variation in the composition of small samples drawn
from a large population
sampling distribution - Answers -is the probability distribution of all possible values of a
sample statistic for a given sample size (n)
estimator - Answers -is a statistic used to infer the value of an unknown population
parameter.
Confidence Interval - Answers -the range of values within which a population parameter
is estimated to lie
Confidence Interval
t distribution - Answers -is used instead of the normal distribution when the population
is bell shaped but the value of the population standard deviation is unknown.
, t distribution characteristics - Answers -are symmetric and bell shaped but have slightly
thicker tails than the normal distribution. The only parameter is degrees of freedom.
df=n-1
Hypothesis tests - Answers -resolve conflicts between two competing opinions
H0 - Answers -defines the null hypothesis
the presumed default state of nature (or status quo)
Ha - Answers -defines the alternative hypothesis
a contradiction of the default state of nature - the research question of interest
Reject H0 - Answers -p value is less than significant level
Can Hypotheses be Proved? - Answers -NO
Hypotheses tests use data from a sample of the population
Without data from the entire population, one cannot "prove" which hypothesis is correct
in the population
Power - Answers -Rejecting the null hypothesis when it is false
1-B
Power Curves - Answers -used to plan studies by ensuring that the power of statistical
tests used will be adequate for the smallest effect size deemed to be of practical
significance in a given context
y=power
x=true unknown value of mu
Two-Sample Tests - Answers -Tests that compare a parameter value across 2 groups.
Samples are taken from each of the 2 target populations.
Sample statistics are used to decide whether the population parameters of the 2 groups
differ significantly.
F test - Answers -The test used to statistically evaluate the differences between the
group means in ANOVA
ANOVA - Answers -analysis of variance is a comparison of MEANS across any number
of groups
seeks to identify sources of variation in Y (a numeric response variable) duding one or
m ore categorical X values
SSB - Answers -explainable differences
SSE - Answers -unexplainable differences
A consistent estimator for the mean: - Answers -converges on the true parameter μ as
the sample size increases.
pi - Answers -is the proportion successes in a binomial distribution
important properties of estimators - Answers -unbiased
efficient
consistent
Central Limit Theorem - Answers -The theory that, as sample size increases, the
distribution of sample means of size n, randomly selected, approaches a normal
distribution.
np>10
n(1-p)>10
Z score for confidence interval - Answers -1.645 1.96 2.576
Type 1 error - Answers -Rejecting null hypothesis when it is true
type 2 error - Answers -failing to reject a false null hypothesis
Twenty randomly selected statistics students were given 15 multiple choice questions
and 15 open-ended questions, all on the same material. The professor was interested in
determining if students scored higher on the multiple choice questions. This experiment
is an example of _______. - Answers -A paired t-test
sampling variation - Answers -the variation in the composition of small samples drawn
from a large population
sampling distribution - Answers -is the probability distribution of all possible values of a
sample statistic for a given sample size (n)
estimator - Answers -is a statistic used to infer the value of an unknown population
parameter.
Confidence Interval - Answers -the range of values within which a population parameter
is estimated to lie
Confidence Interval
t distribution - Answers -is used instead of the normal distribution when the population
is bell shaped but the value of the population standard deviation is unknown.
, t distribution characteristics - Answers -are symmetric and bell shaped but have slightly
thicker tails than the normal distribution. The only parameter is degrees of freedom.
df=n-1
Hypothesis tests - Answers -resolve conflicts between two competing opinions
H0 - Answers -defines the null hypothesis
the presumed default state of nature (or status quo)
Ha - Answers -defines the alternative hypothesis
a contradiction of the default state of nature - the research question of interest
Reject H0 - Answers -p value is less than significant level
Can Hypotheses be Proved? - Answers -NO
Hypotheses tests use data from a sample of the population
Without data from the entire population, one cannot "prove" which hypothesis is correct
in the population
Power - Answers -Rejecting the null hypothesis when it is false
1-B
Power Curves - Answers -used to plan studies by ensuring that the power of statistical
tests used will be adequate for the smallest effect size deemed to be of practical
significance in a given context
y=power
x=true unknown value of mu
Two-Sample Tests - Answers -Tests that compare a parameter value across 2 groups.
Samples are taken from each of the 2 target populations.
Sample statistics are used to decide whether the population parameters of the 2 groups
differ significantly.
F test - Answers -The test used to statistically evaluate the differences between the
group means in ANOVA
ANOVA - Answers -analysis of variance is a comparison of MEANS across any number
of groups
seeks to identify sources of variation in Y (a numeric response variable) duding one or
m ore categorical X values
SSB - Answers -explainable differences
SSE - Answers -unexplainable differences
