MATH 225N Statistics FINAL – Question with all correct Answers (complete solution) 2022 latest update
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
0/1 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's not right.
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.
Your answer:
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.
Content attribution- Opens a dialog
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 = −2.24
Answer Explanation
Correct answers:
$\text{Test statistic = }-2.24$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
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
0/1 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's not right.
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.
Your answer:
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.
Content attribution- Opens a dialog
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 = −2.24
Answer Explanation
Correct answers:
$\text{Test statistic = }-2.24$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
