SOPHIA STATISTICS UNIT 4 MILESTONE
PRACTICE STUDY GUIDE 2026 QUESTIONS
WITH COMPLETE SOLUTIONS GRADED A+
◉ 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.
◉ 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.
Step 1: State the null and alternative hypotheses.
Step 2: Check the conditions necessary in order to actually perform
the inference that you're trying to do.
Step 3: Calculate the test statistic--in this case, a z-statistic--and
calculate the p-value based on the normal sampling distribution.
Step 4: Compare your test statistic to your chosen critical value or
your p-value to our chosen significance level. Those are both
acceptable approaches. Based on how they compare, state a decision
regarding the null hypothesis. Circle it back around to the null
hypothesis and decide if it supports the null hypothesis or refutes
the hypothesis. Make a decision to either reject or fail to reject it
based on your evidence. It should also be in the context of the
problem.
◉ hypothesis test. Answer: Step 1: State the null and alternative
hypotheses.
Step 2: Check the conditions necessary for inference.
, Step 3: Calculate the test statistic and calculate the p-value based on
the normal sampling distribution.
◉ Hypothesis Test for Population Proportions. Answer: A hypothesis
test where we compare to see if the sample proportion of
"successes" differs significantly from a hypothesized value that we
believe is the population proportion of "successes."
◉ Z-test for Population Proportions. Answer: A type of hypothesis
test used to test an assumed population proportion.
Step 1: State the null and alternative hypotheses
Step 2: Check the conditions necessary for inference
Step 3: Calculate the test statistic and the p-value
Step 4: Compare your test statistic to your chosen critical value, or
your p-value to your chosen significance level. Based on how they
compare, state a decision about the null hypothesis and conclusion
in the context of the problem.
◉ critical value. Answer: A value that can be compared to the test
statistic to decide the outcome of a hypothesis test
◉ confidence interval. Answer: An interval that contains likely
values for a parameter. We base our confidence interval on our point
PRACTICE STUDY GUIDE 2026 QUESTIONS
WITH COMPLETE SOLUTIONS GRADED A+
◉ 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.
◉ 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.
Step 1: State the null and alternative hypotheses.
Step 2: Check the conditions necessary in order to actually perform
the inference that you're trying to do.
Step 3: Calculate the test statistic--in this case, a z-statistic--and
calculate the p-value based on the normal sampling distribution.
Step 4: Compare your test statistic to your chosen critical value or
your p-value to our chosen significance level. Those are both
acceptable approaches. Based on how they compare, state a decision
regarding the null hypothesis. Circle it back around to the null
hypothesis and decide if it supports the null hypothesis or refutes
the hypothesis. Make a decision to either reject or fail to reject it
based on your evidence. It should also be in the context of the
problem.
◉ hypothesis test. Answer: Step 1: State the null and alternative
hypotheses.
Step 2: Check the conditions necessary for inference.
, Step 3: Calculate the test statistic and calculate the p-value based on
the normal sampling distribution.
◉ Hypothesis Test for Population Proportions. Answer: A hypothesis
test where we compare to see if the sample proportion of
"successes" differs significantly from a hypothesized value that we
believe is the population proportion of "successes."
◉ Z-test for Population Proportions. Answer: A type of hypothesis
test used to test an assumed population proportion.
Step 1: State the null and alternative hypotheses
Step 2: Check the conditions necessary for inference
Step 3: Calculate the test statistic and the p-value
Step 4: Compare your test statistic to your chosen critical value, or
your p-value to your chosen significance level. Based on how they
compare, state a decision about the null hypothesis and conclusion
in the context of the problem.
◉ critical value. Answer: A value that can be compared to the test
statistic to decide the outcome of a hypothesis test
◉ confidence interval. Answer: An interval that contains likely
values for a parameter. We base our confidence interval on our point
