Quiz 4.1
Name:
Course &section:
I. Read each question carefully and select the letter of the correct answer. Write your answer on the space provided
before each number. NO ERASURES.
1. Which of the following describes a statistical method that uses sample data to test a population hypothesis?
a. Hypothesis testing
b. Null Hypothesis
c. Alternative Hypothesis
d. Mean
2. Which of the following is a reference to the claim that there is no difference, no change, or relationship among
the general population?
a. Hypothesis testing
b. Null Hypothesis
c. Alternative Hypothesis
d. Mean
3. A medical research team is investigating the benefits of a new surgical treatment. One of the claims is that the
mean recovery time for patients after the new treatment is less than 96 hours. Which of the following is the correct set
of hypotheses of the statement?
𝑜 : 𝜇 ≥ 96
a. 𝐻
𝐻 : 𝜇 <96
(𝐶𝑙𝑎𝑖𝑚)
𝑎
𝐻𝑜 : 𝜇 ≥ 96
b. 𝐻
: 𝜇 <96 (𝐶𝑙𝑎𝑖𝑚)
𝑎
𝐻𝑜 : 𝜇 ≤ 96
c. 𝐻
: 𝜇> 96 (𝐶𝑙𝑎𝑖𝑚)
𝑎
𝑜 : 𝜇 ≥ 96(𝐶𝑙𝑎𝑖𝑚)
d. 𝐻
𝐻 : 𝜇> 96
𝑎
4. You are on a research team that is investigating the mean temperature of adult humans. The commonly
accepted claim is that the mean temperature is about 98.6°F. How would you write the null and alternative hypotheses?
𝜇 ≤ 98.6 (𝐶𝑙𝑎𝑖𝑚)
a. 𝐻𝐻𝑜:: 𝜇>
98.6
𝑎
𝑜 : 𝜇 ≥ 98.6
b. 𝐻
𝐻 : 𝜇 <98.6
(𝐶𝑙𝑎𝑖𝑚)
𝑎
98.6
c. 𝐻𝐻𝑜:: 𝜇𝜇 ≠= 98.6
(𝐶𝑙𝑎𝑖𝑚)
𝑎
𝐻𝑜 : 𝜇 = 98.6
d. 𝐻
: 𝜇 ≠ 98.6
(𝐶𝑙𝑎𝑖𝑚)
𝑎
5. When a researcher does not rule out a null hypothesis that is incorrect, which of the following happens?
a. Type I error
b. Type II error
c. level of significance
d. critical value
For numbers 6 – 11, refer to the given problem below.
A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 40 milligrams. You
want to test this claim. During your tests, you find that a random sample of twenty 12-ounce bottles of cola has a mean
caffeine content of 39.2 milligrams. Assume the population is normally distributed and the population standard deviation
is 7.5 milligrams. At a = 0.01, can you reject the company’s claim?
6. What test statistic is the most appropriate to use to test the hypothesis?
a. Left tailed test
b. t – test
c. z -test
d. Right tailed test
7. Which of the following is the correct set of hypotheses for the problem?
𝜇 ≤ 40 (𝐶𝑙𝑎𝑖𝑚)
a. 𝐻𝐻𝑜:: 𝜇>
40
𝑎
𝑜 : 𝜇 ≥ 40
b. 𝐻
𝐻 : 𝜇 <40
(𝐶𝑙𝑎𝑖𝑚)
𝑎
c. 𝐻𝐻𝑜 :: 𝜇𝜇 =≠ 40
40 (𝐶𝑙𝑎𝑖𝑚)
𝑎
(𝐶𝑙𝑎𝑖𝑚)
d. 𝐻𝐻𝑜 :: 𝜇𝜇 =≠ 40
40
𝑎
8. What kind of test is ideal for use in evaluating the hypothesis?
a. Left tailed test
b. two-tailed test
c. z-test
d. Right tailed test
9. What critical value should be applied to the hypothesis?
a. ±1.28
b. 1.28
c. ±2.861
d. 2.539
c. 1.84
d. -1.84
10. What is the test statistic's value?
a. -0.4777
b. 0.4777
11. Which of the following accurately describes the problem's solution?
a. There is enough evidence at 1% level of significance reject the claim that the mean caffeine content per 12ounce bottle of cola is 40 milligrams.
b. There is enough evidence at 10% level of significance reject the claim that the mean caffeine content per 12ounce bottle of cola is 40 milligrams.
c. There is enough evidence at 1% level of significance not to reject the claim that the mean caffeine content per
12-ounce bottle of cola is 40 milligrams.
d. There is enough evidence at 10% level of significance not to reject the claim that the mean caffeine content
per 12-ounce bottle of cola is 40 milligrams.
For numbers 12 – 17, refer to the given problem below.
A scientist estimates that the mean nitrogen dioxide level in Calgary is greater than 32 parts per billion. You want to test
this estimate. To do so, you determine the nitrogen dioxide levels for 34 randomly selected days and have a sample mean
of 30.43. Assume the population standard deviation is 9 parts per billion. At a = 0.05, can you support the scientist’s
estimate?
12. What test statistic is the most appropriate to use to test the hypothesis?
a. Left tailed test
b. t – test
c. z -test
d. Right tailed test
13. Which of the following is the correct set of hypotheses for the problem?
𝑜 : 𝜇 ≤ 32
a. 𝐻
𝐻 : 𝜇> 32
𝑎
(𝐶𝑙𝑎𝑖𝑚)
𝑜 : 𝜇 ≥ 32
b. 𝐻
𝐻 : 𝜇 <32
(𝐶𝑙𝑎𝑖𝑚)
𝑎
c. 𝐻𝐻𝑜 :: 𝜇𝜇 =≠ 32
32 (𝐶𝑙𝑎𝑖𝑚)
𝑎
(𝐶𝑙𝑎𝑖𝑚)
d. 𝐻𝐻𝑜 :: 𝜇𝜇 =≠ 32
32
𝑎
14. What kind of test is ideal for use in evaluating the hypothesis?
a. Left tailed test
b. two-tailed test
c. z-test
d. Right tailed test
15. What critical value should be applied to the hypothesis?
a. -2.492
b. -2.797
c. 1.65
d. -1.65
c. -0.417
d. 0.417
16. What is the test statistic's value?
a. -2.24
b. 2.24
17. Which of the following accurately describes the problem's solution?
a. There is enough evidence at 1% level of significance reject the claim that the mean nitrogen dioxide
level in Calgary is greater than 32 parts per billion.
b. There is enough evidence at 10% level of significance reject the claim that the mean nitrogen dioxide
level in Calgary is greater than 32 parts per billion.
c. There is enough evidence at 5% level of significance not to reject the claim that the mean nitrogen dioxide
level in Calgary is greater than 32 parts per billion.
d. There is enough evidence at 5% level of significance to reject the that the mean nitrogen dioxide
level in Calgary is greater than 32 parts per billion.
18. Find the critical value given n = 12, 𝛼 = 0.10 , left tailed test.
a. -1.796
b. -1.363
c. -1.323
d. -1.721
19. It is the maximum allowable percentage of committing a type I error.
a. 𝛽
b. critical value
c. 𝛼
d. test statistic
20. What can you do if you committed a type 1 error?
a. On the basis of the falsified results, researchers might attempt to construct theories or design new
experiments.
b. The researcher can accept this result and draw the conclusion that the treatment is either ineffective or has a
negligible impact that is not worth further investigation.
c. The experiment can be repeated using the same number of samples, and the researcher can then attempt to
show that the treatment is effective.
c. It is a waste of time for the researchers to try and accomplish anything.
Quiz 4.1
Name:
Course &section:
I. Read each question carefully and select the letter of the correct answer. Write your answer on the space provided
before each number. NO ERASURES.
1. Which of the following best sums up a statistical approach that tests a population hypothesis using sample
data?
a. Hypothesis testing
b. Null Hypothesis
c. Alternative Hypothesis
d. Mean
2. Which of the following refers to the assertion that there is a difference, distinction, or connection between the
population as a whole?
a. Hypothesis testing
b. Null Hypothesis
c. Alternative Hypothesis
d. Mean
3. A medical research team is investigating the benefits of a new surgical treatment. One of the claims is that the
mean recovery time for patients after the new treatment is at least 96 hours. Which of the following is the correct set of
hypotheses of the statement?
𝑜 : 𝜇 ≥ 96
a. 𝐻
𝐻 : 𝜇 <96
(𝐶𝑙𝑎𝑖𝑚)
𝑎
𝐻𝑜 : 𝜇 ≥ 96
b. 𝐻
: 𝜇 <96 (𝐶𝑙𝑎𝑖𝑚)
𝑎
𝐻𝑜 : 𝜇 ≤ 96
c. 𝐻
: 𝜇> 96 (𝐶𝑙𝑎𝑖𝑚)
𝑎
𝑜 : 𝜇 ≥ 96(𝐶𝑙𝑎𝑖𝑚)
d. 𝐻
𝐻 : 𝜇> 96
𝑎
4. You are on a research team that is investigating the mean temperature of adult humans. The commonly
accepted claim is that the mean temperature is not less than 98.6°F. How would you write the null and alternative
hypotheses?
𝜇 ≤ 98.6 (𝐶𝑙𝑎𝑖𝑚)
a. 𝐻𝐻𝑜:: 𝜇>
98.6
𝑎
𝑜 : 𝜇 ≥ 98.6
b. 𝐻
𝐻 : 𝜇 <98.6
(𝐶𝑙𝑎𝑖𝑚)
𝑎
98.6
c. 𝐻𝐻𝑜:: 𝜇𝜇 ≠= 98.6
(𝐶𝑙𝑎𝑖𝑚)
𝑎
𝐻𝑜 : 𝜇 = 98.6
d. 𝐻
: 𝜇 ≠ 98.6
(𝐶𝑙𝑎𝑖𝑚)
𝑎
5. What happens when a researcher disregards a null hypothesis that is valid?
a. Type I error
b. Type II error
c. level of significance
d. critical value
For numbers 6 – 11, refer to the given problem below.
A fast-food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 920
milligrams. A random sample of 44 breakfast sandwiches has a mean sodium content of 925 milligrams. Assume the
population standard deviation is 18 milligrams. At a = 0.10, do you have enough evidence to reject the restaurant’s
claim??
6. What test statistic is the most appropriate to use to test the hypothesis?
a. Left tailed test
b. t – test
c. z -test
d. Right tailed test
7. Which of the following is the correct set of hypotheses for the problem?
𝜇 ≤ 920 (𝐶𝑙𝑎𝑖𝑚)
a. 𝐻𝐻𝑜:: 𝜇>
920
𝑎
𝑜 : 𝜇 ≥ 920
b. 𝐻
𝐻 : 𝜇 <920
(𝐶𝑙𝑎𝑖𝑚)
𝑎
c. 𝐻𝐻𝑜 :: 𝜇𝜇 =≠ 920
920 (𝐶𝑙𝑎𝑖𝑚)
𝑎
(𝐶𝑙𝑎𝑖𝑚)
d. 𝐻𝐻𝑜 :: 𝜇𝜇 =≠ 920
920
𝑎
8. What kind of test is ideal for use in evaluating the hypothesis?
a. Left tailed test
b. two-tailed test
c. z-test
d. Right tailed test
9. What critical value should be applied to the hypothesis?
a. ±1.28
b. 1.28
c. ±2.861
d. 2.539
c. 1.84
d. -1.84
10. What is the test statistic's value?
a. -0.4777
b. 0.4777
11. Which of the following accurately describes the problem's solution?
a. There is enough evidence at 10% level of significance not to reject the claim that the mean sodium content in
one of its breakfast sandwiches is no more than 920 milligrams.
b. There is enough evidence at 10% level of significance reject the claim that the mean sodium content in one of
its breakfast sandwiches is no more than 920 milligrams.
c. There is enough evidence at 1% level of significance not to reject the claim that the mean sodium
content in one of its breakfast sandwiches is no more than 920 milligrams.
d. There is enough evidence at 1% level of significance to reject the claim that the mean sodium content in
one of its breakfast sandwiches is no more than 920 milligrams.
For numbers 12 – 17, refer to the given problem below.
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 750 hours. A random
sample of 25 light bulbs has a mean life of 745 hours. Assume the population is normally distributed and the population
standard deviation is 60 hours. At a = 0.01, do you have enough evidence to reject the manufacturer’s claim?
12. What test statistic is the most appropriate to use to test the hypothesis?
a. Left tailed test
b. t – test
c. z -test
13. Which of the following is the correct set of hypotheses for the problem?
d. Right tailed test
𝑜 : 𝜇 ≤ 750
a. 𝐻
𝐻 : 𝜇> 750
𝑎
(𝐶𝑙𝑎𝑖𝑚)
𝐻𝑜 : 𝜇= 750
b. 𝐻
: 𝜇 ≠750
(𝐶𝑙𝑎𝑖𝑚)
𝑎
c. 𝐻𝐻𝑜 :: 𝜇𝜇 =≠ 750
750 (𝐶𝑙𝑎𝑖𝑚)
𝑎
(𝐶𝑙𝑎𝑖𝑚)
d. 𝐻𝐻𝑜 :: 𝜇𝜇<≥ 750
750
𝑎
14. What kind of test is ideal for use in evaluating the hypothesis?
a. Left tailed test
b. two-tailed test
c. z-test
d. Right tailed test
15. What critical value should be applied to the hypothesis?
a. -2.492
b. -2.797
c. 1.65
d. -1.65
c. -0.417
d. 0.417
16. What is the test statistic's value?
a. -2.24
b. 2.24
17. Which of the following accurately describes the problem's solution?
a. There is enough evidence at 1% level of significance reject the claim that the mean life of a certain type of light
bulb is at least 750 hours.
b. There is enough evidence at 10% level of significance reject the claim that the mean life of a certain type of
light bulb is at least 750 hours.
c. There is enough evidence at 1% level of significance not to reject the claim that the mean life of a certain type
of light bulb is at least 750 hours.
d. There is enough evidence at 5% level of significance to reject the that the mean life of a certain type of light
bulb is at least 750 hours.
18. Find the critical value given n = 22, 𝛼 = 0.10 , left tailed test.
a. -1.796
b. -1.363
c. -1.323
d. -1.721
19. It is the maximum allowable percentage of committing a type II error.
a. 𝛽
b. critical value
c. 𝛼
d. test statistic
20. What can you do if you committed a type II error?
a. On the basis of the falsified results, researchers might attempt to construct theories or design new
experiments.
b. The researcher can accept this result and draw the conclusion that the treatment is either ineffective or has a
negligible impact that is not worth further investigation.
c. The experiment can be repeated using the same number of samples, and the researcher can then attempt to
show that the treatment is effective.
c. It is a waste of time for the researchers to try and accomplish anything.