MATH225 Week 8 Final Exam
Question 1
1/1 points
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.
That is correct!
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
1/1 points
The answer choices below represent different hypothesis tests. Which of the choices are right-
tailed tests? Select all correct answers.
That is correct!
,
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
1/1 points
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.
That is correct!
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.
Question 4
1/1 points
Suppose a chef claims that her meatball weight is less than 4 ounces, on average. Several of her
customers do not believe her, so the chef decides to do a hypothesis test, at a 10% significance
level, to persuade them. She cooks 14 meatballs. The mean weight of the sample meatballs is 3.7
ounces. The chef knows from experience that the standard deviation for her meatball weight is
0.5 ounces.
H0: μ≥4; Ha: μ<4
α=0.1 (significance level)
What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal
places?
That is correct!
Test statistic = minus 2 point 2 4$$
Test statistic = minus 2 point 2 4 - correct
Answer Explanation
Correct answers:
Test statistic = minus 2 point 2 4 $\text{Test statistic = }-2.24$
The hypotheses were chosen, and the significance level was decided on, so the next step in
hypothesis testing is to compute the test statistic. In this scenario, the sample mean weight,
x¯=3.7. The sample the chef uses is 14 meatballs, so n=14. She knows the standard deviation of
the meatballs, σ=0.5. Lastly, the chef is comparing the population mean weight to 4 ounces. So,
this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values
into the formula to compute the test statistic:
Question 1
1/1 points
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.
That is correct!
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
1/1 points
The answer choices below represent different hypothesis tests. Which of the choices are right-
tailed tests? Select all correct answers.
That is correct!
,
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
1/1 points
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.
That is correct!
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.
Question 4
1/1 points
Suppose a chef claims that her meatball weight is less than 4 ounces, on average. Several of her
customers do not believe her, so the chef decides to do a hypothesis test, at a 10% significance
level, to persuade them. She cooks 14 meatballs. The mean weight of the sample meatballs is 3.7
ounces. The chef knows from experience that the standard deviation for her meatball weight is
0.5 ounces.
H0: μ≥4; Ha: μ<4
α=0.1 (significance level)
What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal
places?
That is correct!
Test statistic = minus 2 point 2 4$$
Test statistic = minus 2 point 2 4 - correct
Answer Explanation
Correct answers:
Test statistic = minus 2 point 2 4 $\text{Test statistic = }-2.24$
The hypotheses were chosen, and the significance level was decided on, so the next step in
hypothesis testing is to compute the test statistic. In this scenario, the sample mean weight,
x¯=3.7. The sample the chef uses is 14 meatballs, so n=14. She knows the standard deviation of
the meatballs, σ=0.5. Lastly, the chef is comparing the population mean weight to 4 ounces. So,
this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values
into the formula to compute the test statistic:
