FOUNDATIONS OF STATISTICS MILESTONE WITH
RATIONALES
1
Which graph correctly matches a probability value with the shaded
region between z-scores?
•
•
•
•
RATIONALE
Remember the 68/95/99.7 rule where 68% of the data lies within 1 standard
deviation, 95% of the data falls within 2 standard deviations of the mean,
and 99.7% of the data falls within 3 standard deviations of the mean.
CONCEPT
, FOUNDATIONS OF STATISTICS MILESTONE WITH
RATIONALES
Standard Normal Distribution
2
, FOUNDATIONS OF STATISTICS MILESTONE WITH
RATIONALES
Ahmad was conducting some tests to determine if there was a relationship
between taking sleeping pills and the amount of sleep a person gets. His null
hypothesis was that taking sleeping pills did not have any effect on the
amount of sleep a person receives. Ahmad's alternate hypothesis was that
taking sleeping pills increases the amount of sleep a person will get.
If Ahmad completed his study, which of the following statements
would indicate a Type II error?
• Ahmad's results showed that sleeping pills caused people to get more
sleep, and in fact sleeping pills and the amount of sleep people were
getting did have a positive cause and effect relationship.
• Ahmad's results showed that taking sleeping pills did increase the
amount of sleep people were getting when in fact sleeping pills were
not affecting sleep.
• Ahmad's results showed that sleeping pills did not affect the amount of
sleep participants were getting when in fact there was not a cause and
effect relationship between the two variables.
• Ahmad's results showed that sleeping pills did not affect the amount of
sleep participants were getting when in fact sleeping pills were
increasing the sleep people were getting.
RATIONALE
Recall that Type II error is when we fail to reject the null when it is false. In
this case, if we determined that the pills had no effect on the amount of
sleep, when they really did, it would be a Type II error.
CONCEPT
Type I and Type II Errors
3
RATIONALES
1
Which graph correctly matches a probability value with the shaded
region between z-scores?
•
•
•
•
RATIONALE
Remember the 68/95/99.7 rule where 68% of the data lies within 1 standard
deviation, 95% of the data falls within 2 standard deviations of the mean,
and 99.7% of the data falls within 3 standard deviations of the mean.
CONCEPT
, FOUNDATIONS OF STATISTICS MILESTONE WITH
RATIONALES
Standard Normal Distribution
2
, FOUNDATIONS OF STATISTICS MILESTONE WITH
RATIONALES
Ahmad was conducting some tests to determine if there was a relationship
between taking sleeping pills and the amount of sleep a person gets. His null
hypothesis was that taking sleeping pills did not have any effect on the
amount of sleep a person receives. Ahmad's alternate hypothesis was that
taking sleeping pills increases the amount of sleep a person will get.
If Ahmad completed his study, which of the following statements
would indicate a Type II error?
• Ahmad's results showed that sleeping pills caused people to get more
sleep, and in fact sleeping pills and the amount of sleep people were
getting did have a positive cause and effect relationship.
• Ahmad's results showed that taking sleeping pills did increase the
amount of sleep people were getting when in fact sleeping pills were
not affecting sleep.
• Ahmad's results showed that sleeping pills did not affect the amount of
sleep participants were getting when in fact there was not a cause and
effect relationship between the two variables.
• Ahmad's results showed that sleeping pills did not affect the amount of
sleep participants were getting when in fact sleeping pills were
increasing the sleep people were getting.
RATIONALE
Recall that Type II error is when we fail to reject the null when it is false. In
this case, if we determined that the pills had no effect on the amount of
sleep, when they really did, it would be a Type II error.
CONCEPT
Type I and Type II Errors
3
