(Answered) Stats Sophia 5, Statistics Sophia 4,
Statistics Sophia 2, Statistics Sophia 1.1 Exam/
300 Q&A.
sample statistic - Answer: A measure of an attribute of a sample.
sample mean - Answer: A mean obtained from a sample of a given size. Denoted as x bar.
population parameters - Answer: Summary values for the population. These are often
unknown.
population mean - Answer: A mean for all values in the population. Denoted as μ.
sampling with replacement - Answer: A sampling plan where each observation that is sampled
is replaced after each time it is sampled, resulting in an observation being able to be selected
more than once.
Page 1 of 39
,sampling error - Answer: The amount by which the sample statistic differs from the population
parameter.
sample size - Answer: The size of a sample of a population of interest.
distribution of sample means - Answer: Step 1: First, take these sample means and graph them.
Draw out an axis. For this one, it should go from 1 to 4 because this set can't average anything
higher than four or lower than a one.
Step 2: Take the average value, for example, the mean of 2.5, and put a dot at 2.5 on the x-axis,
much like a dot plot. Do this for all the sample means that you have found.
Step 3: You can keep doing this over and over again. Ideally, you would do this hundreds or
thousands of times, to show the distribution of all possible samples that could be taken of size
four. Once you've enumerated every possible sample of size four from this spinner, then the
sampling distribution looks like this:
A distribution where each data point consists of a mean of a collected sample. For a given
sample size, every possible sample mean will be plotted in the distribution.
Standard Deviation of a Distribution of Sample Means - Answer: The standard deviation of the
population, divided by the square root of sample size.
standard error - Answer: The standard deviation of the sampling distribution of sample means.
central limit theorem - Answer: A theorem that explains the shape of a sampling distribution of
sample means. It states that if the sample size is large (generally n ≥ 30), and the standard
deviation of the population is finite, then the distribution of sample means will be
approximately normal.
Page 2 of 39
,Distribution of Sample Proportions - Answer: The distribution of all possible sample proportions
for a certain size, n.
hypothesis testing - Answer: The standard procedure in statistics for testing claims about
population parameters.
hypothesis - Answer: A claim about a population parameter.
null hypothesis - Answer: A claim about a particular value of a population parameter that serves
as the starting assumption for a hypothesis test.
alternative hypothesis - Answer: A claim that a population parameter differs from the value
claimed in the null hypothesis.
statistical significance - Answer: The statistic obtained is so different from the hypothesized
value that we are unable to attribute the difference to chance variation.
practical significance - Answer: An arbitrary assessment of whether observations reflect a
practical real-world use.
type 1 error - Answer: An error that occurs when a true null hypothesis is rejected.
type 2 error - Answer: An error that occurs when a false null hypothesis is not rejected.
significance level - Answer: The probability of making a Type I error. Abbreviated with the
symbol, alpha.
Power of a Hypothesis Test - Answer: The probability that we reject the null hypothesis
(correctly) when a difference truly does exist.
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, one-tailed test - Answer: A test for when you have reason to believe the population parameter
is higher or lower than the assumed parameter value of the null hypothesis.
right-tailed test - Answer: A hypothesis test where the alternative hypothesis only states that
the parameter is higher than the stated value from the null hypothesis.
left-tailed test - Answer: A hypothesis test where the alternative hypothesis only states that the
parameter is lower than the stated value from the null hypothesis.
two-tailed test - Answer: A test for when you have reason to believe the population parameter
is different from the assumed parameter value of the null hypothesis
test statistic - Answer: A measurement, in standardized units, of how far a sample statistic is
from the assumed parameter if the null hypothesis is true
statistic - parameter / standard deviation of statistic
p-value - Answer: The probability that the test statistic is that value or more extreme in the
direction of the alternative hypothesis
critical value - Answer: A value that can be compared to the test statistic to decide the outcome
of a hypothesis test
standard normal table - Answer: A table showing the values of the cumulative distribution
function of the standard normal distribution.
Z-Test for Population Means - Answer: A hypothesis test that compares a hypothesized mean
from the null hypothesis to a sample mean, when the population standard deviation is known.
Page 4 of 39
Statistics Sophia 2, Statistics Sophia 1.1 Exam/
300 Q&A.
sample statistic - Answer: A measure of an attribute of a sample.
sample mean - Answer: A mean obtained from a sample of a given size. Denoted as x bar.
population parameters - Answer: Summary values for the population. These are often
unknown.
population mean - Answer: A mean for all values in the population. Denoted as μ.
sampling with replacement - Answer: A sampling plan where each observation that is sampled
is replaced after each time it is sampled, resulting in an observation being able to be selected
more than once.
Page 1 of 39
,sampling error - Answer: The amount by which the sample statistic differs from the population
parameter.
sample size - Answer: The size of a sample of a population of interest.
distribution of sample means - Answer: Step 1: First, take these sample means and graph them.
Draw out an axis. For this one, it should go from 1 to 4 because this set can't average anything
higher than four or lower than a one.
Step 2: Take the average value, for example, the mean of 2.5, and put a dot at 2.5 on the x-axis,
much like a dot plot. Do this for all the sample means that you have found.
Step 3: You can keep doing this over and over again. Ideally, you would do this hundreds or
thousands of times, to show the distribution of all possible samples that could be taken of size
four. Once you've enumerated every possible sample of size four from this spinner, then the
sampling distribution looks like this:
A distribution where each data point consists of a mean of a collected sample. For a given
sample size, every possible sample mean will be plotted in the distribution.
Standard Deviation of a Distribution of Sample Means - Answer: The standard deviation of the
population, divided by the square root of sample size.
standard error - Answer: The standard deviation of the sampling distribution of sample means.
central limit theorem - Answer: A theorem that explains the shape of a sampling distribution of
sample means. It states that if the sample size is large (generally n ≥ 30), and the standard
deviation of the population is finite, then the distribution of sample means will be
approximately normal.
Page 2 of 39
,Distribution of Sample Proportions - Answer: The distribution of all possible sample proportions
for a certain size, n.
hypothesis testing - Answer: The standard procedure in statistics for testing claims about
population parameters.
hypothesis - Answer: A claim about a population parameter.
null hypothesis - Answer: A claim about a particular value of a population parameter that serves
as the starting assumption for a hypothesis test.
alternative hypothesis - Answer: A claim that a population parameter differs from the value
claimed in the null hypothesis.
statistical significance - Answer: The statistic obtained is so different from the hypothesized
value that we are unable to attribute the difference to chance variation.
practical significance - Answer: An arbitrary assessment of whether observations reflect a
practical real-world use.
type 1 error - Answer: An error that occurs when a true null hypothesis is rejected.
type 2 error - Answer: An error that occurs when a false null hypothesis is not rejected.
significance level - Answer: The probability of making a Type I error. Abbreviated with the
symbol, alpha.
Power of a Hypothesis Test - Answer: The probability that we reject the null hypothesis
(correctly) when a difference truly does exist.
Page 3 of 39
, one-tailed test - Answer: A test for when you have reason to believe the population parameter
is higher or lower than the assumed parameter value of the null hypothesis.
right-tailed test - Answer: A hypothesis test where the alternative hypothesis only states that
the parameter is higher than the stated value from the null hypothesis.
left-tailed test - Answer: A hypothesis test where the alternative hypothesis only states that the
parameter is lower than the stated value from the null hypothesis.
two-tailed test - Answer: A test for when you have reason to believe the population parameter
is different from the assumed parameter value of the null hypothesis
test statistic - Answer: A measurement, in standardized units, of how far a sample statistic is
from the assumed parameter if the null hypothesis is true
statistic - parameter / standard deviation of statistic
p-value - Answer: The probability that the test statistic is that value or more extreme in the
direction of the alternative hypothesis
critical value - Answer: A value that can be compared to the test statistic to decide the outcome
of a hypothesis test
standard normal table - Answer: A table showing the values of the cumulative distribution
function of the standard normal distribution.
Z-Test for Population Means - Answer: A hypothesis test that compares a hypothesized mean
from the null hypothesis to a sample mean, when the population standard deviation is known.
Page 4 of 39
