MATH225 WEEK 8 FINAL EXAM
(VERSION 1, 2, 3, 4)
, MATH225 WEEK 8 FINAL EXAM
VERSION 1
QUESTION 1
A fitness center claims that the mean amount of time that a person spends at the gym
per visit is 33 minutes. Identify the null hypothesis, H0, and the alternative
hypothesis, Ha, in terms of the parameter μ.
H0: μ≠33; Ha: μ=33
H0: μ=33; Ha: μ≠33
H0: μ≥33; Ha: μ<33
H0: μ≤33; Ha: μ>33
Answer Explanation
Correct answer:
H0: μ=33; Ha: μ≠33
Let the parameter μ be used to represent the mean. The null hypothesis is always
stated with some form of equality: equal (=), greater than or equal to (≥), or less than
or equal to (≤). Therefore, in this case, the null hypothesis H0 is μ=33. The
alternative hypothesis is contradictory to the null hypothesis, so Ha is μ≠33.
QUESTION 2
The answer choices below represent different hypothesis tests. Which of the choices
are right-tailed tests? Select all correct answers.
H0:X≥17.1, Ha:X<17.1
,
H0:X=14.4, Ha:X≠14.4
H0:X≤3.8, Ha:X>3.8
H0:X≤7.4, Ha:X>7.4
H0:X=3.3, Ha:X≠3.3
Answer Explanation
Correct answer:
H0:X≤3.8, Ha:X>3.8
H0:X≤7.4, Ha:X>7.4
Remember the forms of the hypothesis tests.
Right-tailed: H0:X≤X0, Ha:X>X0.
Left-tailed: H0:X≥X0, Ha:X<X0.
Two-tailed: H0:X=X0, Ha:X≠X0.
, So in this case, the right-tailed tests are:
H0:X≤7.4, Ha:X>7.4
H0:X≤3.8, Ha:X>3.8
QUESTION 3
Find the Type II error given that the null hypothesis, H0, is: a building inspector claims
that no more than 15% of structures in the county were built without permits.
The building inspector thinks that no more than 15% of the structures in the county
were built without permits when, in fact, no more than 15% of the structures really were
built without permits.
The building inspector thinks that more than 15% of the structures in the county were
built without permits when, in fact, more than 15% of the structures really were built
without permits.
The building inspector thinks that more than 15% of the structures in the county were
built without permits when, in fact, at most 15% of the structures were built without
permits.
The building inspector thinks that no more than 15% of the structures in the county
were built without permits when, in fact, more than 15% of the structures were built
without permits.
Answer Explanation
Correct answer:
The building inspector thinks that no more than 15% of the structures in the county
were built without permits when, in fact, more than 15% of the structures were built
without permits.
A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In
this case, the Type II error is when the building inspector thinks that no more
than 15% of the structures were built without permits when, in fact, more
than 15% of the structures were built without permits.
(VERSION 1, 2, 3, 4)
, MATH225 WEEK 8 FINAL EXAM
VERSION 1
QUESTION 1
A fitness center claims that the mean amount of time that a person spends at the gym
per visit is 33 minutes. Identify the null hypothesis, H0, and the alternative
hypothesis, Ha, in terms of the parameter μ.
H0: μ≠33; Ha: μ=33
H0: μ=33; Ha: μ≠33
H0: μ≥33; Ha: μ<33
H0: μ≤33; Ha: μ>33
Answer Explanation
Correct answer:
H0: μ=33; Ha: μ≠33
Let the parameter μ be used to represent the mean. The null hypothesis is always
stated with some form of equality: equal (=), greater than or equal to (≥), or less than
or equal to (≤). Therefore, in this case, the null hypothesis H0 is μ=33. The
alternative hypothesis is contradictory to the null hypothesis, so Ha is μ≠33.
QUESTION 2
The answer choices below represent different hypothesis tests. Which of the choices
are right-tailed tests? Select all correct answers.
H0:X≥17.1, Ha:X<17.1
,
H0:X=14.4, Ha:X≠14.4
H0:X≤3.8, Ha:X>3.8
H0:X≤7.4, Ha:X>7.4
H0:X=3.3, Ha:X≠3.3
Answer Explanation
Correct answer:
H0:X≤3.8, Ha:X>3.8
H0:X≤7.4, Ha:X>7.4
Remember the forms of the hypothesis tests.
Right-tailed: H0:X≤X0, Ha:X>X0.
Left-tailed: H0:X≥X0, Ha:X<X0.
Two-tailed: H0:X=X0, Ha:X≠X0.
, So in this case, the right-tailed tests are:
H0:X≤7.4, Ha:X>7.4
H0:X≤3.8, Ha:X>3.8
QUESTION 3
Find the Type II error given that the null hypothesis, H0, is: a building inspector claims
that no more than 15% of structures in the county were built without permits.
The building inspector thinks that no more than 15% of the structures in the county
were built without permits when, in fact, no more than 15% of the structures really were
built without permits.
The building inspector thinks that more than 15% of the structures in the county were
built without permits when, in fact, more than 15% of the structures really were built
without permits.
The building inspector thinks that more than 15% of the structures in the county were
built without permits when, in fact, at most 15% of the structures were built without
permits.
The building inspector thinks that no more than 15% of the structures in the county
were built without permits when, in fact, more than 15% of the structures were built
without permits.
Answer Explanation
Correct answer:
The building inspector thinks that no more than 15% of the structures in the county
were built without permits when, in fact, more than 15% of the structures were built
without permits.
A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In
this case, the Type II error is when the building inspector thinks that no more
than 15% of the structures were built without permits when, in fact, more
than 15% of the structures were built without permits.
