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MATH 110 M7 EXAM INTRODUCTION TO STATISTICS
2025 QUESTIONS AND ANSWERS/ MATH 110
MODULE 7 PROBLEM SET
null hypothesis - ...ANSWER...✓✓ (H0) is the foundational
assumption about a population and represents the status
quo. It is a statement of equality (==).
alternative hypothesis - ...ANSWER...✓✓ (Ha) is a
different assumption about a population and is a
statement of inequality (<<, >>, or ≠≠). Using a hypothesis
test, we determine whether it is more likely that the null
hypothesis or the alternative hypothesis is true.
P-value - ...ANSWER...✓✓ is the probability of getting a
test statistic at least as extreme as the one you got,
assuming H0H0 is true. A PP-value is calculated by
finding the area under the normal distribution curve that
is more extreme (farther away from the mean) than the
z-score. The alternative hypothesis tells us whether we
look at both tails or only one.
The level of significance - ...ANSWER...✓✓ (αα) is the
standard for determining whether or not the null
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hypothesis should be rejected. Typical values for αα are
0.050.05, 0.100.10, and 0.010.01. If the PP-value is less than
αα we reject the null. If the PP-value is not less than αα
we fail to reject the null.
Type I error - ...ANSWER...✓✓ is committed when we
reject a null hypothesis that is, in reality, true
Type II error - ...ANSWER...✓✓ is committed when we fail
to reject a null hypothesis that is, in reality, not true.
The value of αα is - ...ANSWER...✓✓ the probability of
committing a Type I error.
confidence interval - ...ANSWER...✓✓ Range of values
that has a set probability of containing the "true" value.
Help determine the validity of the sample statistic
margin of error formula - ...ANSWER...✓✓ m is z* (sigma/
Square root n)
confidence interval formula - ...ANSWER...✓✓
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sample size formula - ...ANSWER...✓✓ n=(z∗σ/m)2
Suppose you were also asked to calculate a 90%
confidence interval. What would change from the 95%
confidence interval you calculated previously? -
...ANSWER...✓✓ The 90% confidence interval would be
narrower.
if sample size is larger then the confidence interval is -
...ANSWER...✓✓ narrower
if sample size is smaller then the confidence interval is -
...ANSWER...✓✓ wider
degrees of freedom - ...ANSWER...✓✓ The number of
individual scores that can vary without changing the
sample mean. Statistically written as 'N-1' where N
represents the number of subjects.
t distribution - ...ANSWER...✓✓ x-m/(a/Square root n)
MATH 110 M7 EXAM INTRODUCTION TO STATISTICS
2025 QUESTIONS AND ANSWERS/ MATH 110
MODULE 7 PROBLEM SET
null hypothesis - ...ANSWER...✓✓ (H0) is the foundational
assumption about a population and represents the status
quo. It is a statement of equality (==).
alternative hypothesis - ...ANSWER...✓✓ (Ha) is a
different assumption about a population and is a
statement of inequality (<<, >>, or ≠≠). Using a hypothesis
test, we determine whether it is more likely that the null
hypothesis or the alternative hypothesis is true.
P-value - ...ANSWER...✓✓ is the probability of getting a
test statistic at least as extreme as the one you got,
assuming H0H0 is true. A PP-value is calculated by
finding the area under the normal distribution curve that
is more extreme (farther away from the mean) than the
z-score. The alternative hypothesis tells us whether we
look at both tails or only one.
The level of significance - ...ANSWER...✓✓ (αα) is the
standard for determining whether or not the null
,2|Page
hypothesis should be rejected. Typical values for αα are
0.050.05, 0.100.10, and 0.010.01. If the PP-value is less than
αα we reject the null. If the PP-value is not less than αα
we fail to reject the null.
Type I error - ...ANSWER...✓✓ is committed when we
reject a null hypothesis that is, in reality, true
Type II error - ...ANSWER...✓✓ is committed when we fail
to reject a null hypothesis that is, in reality, not true.
The value of αα is - ...ANSWER...✓✓ the probability of
committing a Type I error.
confidence interval - ...ANSWER...✓✓ Range of values
that has a set probability of containing the "true" value.
Help determine the validity of the sample statistic
margin of error formula - ...ANSWER...✓✓ m is z* (sigma/
Square root n)
confidence interval formula - ...ANSWER...✓✓
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sample size formula - ...ANSWER...✓✓ n=(z∗σ/m)2
Suppose you were also asked to calculate a 90%
confidence interval. What would change from the 95%
confidence interval you calculated previously? -
...ANSWER...✓✓ The 90% confidence interval would be
narrower.
if sample size is larger then the confidence interval is -
...ANSWER...✓✓ narrower
if sample size is smaller then the confidence interval is -
...ANSWER...✓✓ wider
degrees of freedom - ...ANSWER...✓✓ The number of
individual scores that can vary without changing the
sample mean. Statistically written as 'N-1' where N
represents the number of subjects.
t distribution - ...ANSWER...✓✓ x-m/(a/Square root n)
