AnswersProbability and Statistics with Applications Honors Sem-2-FL-1210300 2024-2025Significance Tests and Confidence Intervals

Significance Tests and Confidence Intervals Answers

10 verified answers
1
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A study was conducted to determine the true mean hourly wage of all working high school students. A 95% confidence interval for the true mean hourly wage of high school students is ($6.50, $13.00). Based upon this interval, what conclusion should be made about the hypotheses: = 15 versus where = the true mean hourly income of all working high school students at α = 0.05?

Question illustration
A
Reject H0. Since 15 falls outside the 95% confidence interval, there is convincing evidence that the true mean hourly income of all working high school students is greater than $15.
B
Reject H0. Since 15 falls outside the 95% confidence interval, there is convincing evidence that the true mean hourly income of all working high school students is different than $15.
C
Fail to reject H0. Since 15 falls outside the 95% confidence interval, there is convincing evidence that the true mean hourly income of all working high school students is greater than $15.
D
Fail to reject H0. Since 15 falls outside the 95% confidence interval, there is convincing evidence that the true mean hourly income of all working high school students is different than $15.
2
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The power of a significance test to reject the null hypothesis when a particular value of the alternative is true is 0.8. What is the probability that this test results in a Type II error?

A
0.01
B
0.05
C
0.20
D
0.80
3

On average, a person’s body temperature should be approximately 98.6°F. A doctor would like to test the hypotheses versus where μ = the true mean body temperature of all adults. A 99% confidence interval based upon a random sample of 100 adults is (97.5, 99.2). Using the interval, can the researcher reject the null hypothesis?

Question illustration
A
Yes, the null hypothesis can be rejected at the significance level α = 0.01, because 98.6 is contained in the 99% confidence interval.
B
Yes, the null hypothesis can be rejected at the significance level α = 0.005, because 98.6 is contained in the 99% confidence interval.
C
No, the null hypothesis cannot be rejected at the significance level α = 0.01, because 98.6 is contained in the 99% confidence interval.
D
No, the null hypothesis cannot be rejected at the significance level α = 0.005, because 98.6 is contained in the 99% confidence interval.
4

A social scientist collects information about study time for a random sample of 40 students with the intention of testing the hypotheses = 2 hours per night versus 2 hours per night where = the true mean number of hours of study time per night for students.Rather than test these hypotheses, she computes the 90% confidence interval, (1.5, 1.8). Based upon the confidence interval, what conclusion can be made using = 0.10?

Question illustration
A
She should reject the null hypothesis. Since 2 falls outside of the 90% confidence interval, there is convincing evidence that the true mean number of hours of study time per night for students differs from 2 hours per night.
B
She should reject the null hypothesis. Since 2 falls outside of the 90% confidence interval, there is not convincing evidence that the true mean number of hours of study time per night for students differs from 2 hours per night.
C
She should fail to reject the null hypothesis. Since 2 falls outside of the 90% confidence interval, there is convincing evidence that the true mean number of hours of study time per night for students differs from 2 hours per night.
D
She should fail to reject the null hypothesis. Since 2 falls outside of the 90% confidence interval, there is not convincing evidence that the true mean number of hours of study time per night for students differs from 2 hours per night.
5

A school newspaper article claims that the mean weight of student backpacks is 20 pounds. A student of this school would like to test the hypotheses = 20 versus 20 where μ = the true mean weight of all backpacks using a random sample of 30 students. The power of this test to reject the null hypothesis when μ = 19.5 is 0.78 when a significance level of 0.05 is used. Which of the following would increase the power of this test?

Question illustration
A
decrease the significance level to 0.01
B
decrease the sample size to 25 students
C
increase the sample size to 50 students
D
increase the alternative value of the parameter to μ = 19.75
6

An engineer would like to design a parking garage in the most cost-effective manner. The garage must be able to fit pickup trucks, which have an average height of 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random sample of 100 trucks, which will be used to determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches.

A
n = 50, alpha = 0.01
Option A
B
n = 50, alpha = 0.10
Option B
C
n = 200, alpha = 0.01
Option C
D
n = 200, alpha = 0.10
Option D
7

A social scientist collects information about study time for a random sample of 40 students with the intention of testing the hypotheses = 2 hours per night versus 2 hours per night where μ = the true mean number of hours of study time per night for students. The power of this test to reject the null hypothesis when μ = 2.25 is 0.35. What is the correct interpretation of the value 0.35?

Question illustration
A
The probability that this test will reject that the true mean number of hours of study time per night for students is 2 when the true mean is not 2.25 is 0.35.
B
The probability that this test will reject that the true mean number of hours of study time per night for students is 2 when the true mean is really 2.25 is 0.35.
C
The probability that this test will fail to reject that the true mean number of hours of study time per night for students is 2 when the true mean is not 2.25 is 0.35.
D
The probability that this test will fail to reject that the true mean number of hours of study time per night for students is 2 when the true mean is really 2.25 is 0.35.
8

A study was conducted to determine the true mean weight of all packages shipped by a company. A 90% confidence interval for the true mean weight is 4.9 pounds to 14.8 pounds. Based upon this interval, what decision should be made about the hypotheses: =5 versus 5 where μ = the true mean weight of all packages at α = 0.10?

Question illustration
A
The null hypothesis should be rejected, because 5 falls inside the 90% confidence interval.
B
The null hypothesis should be rejected, because 5 falls outside the 90% confidence interval.
C
The null hypothesis should not be rejected, because 5 falls inside the 90% confidence interval.
D
The null hypothesis should not be rejected, because 5 falls outside the 90% confidence interval.
9

A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students who are currently taking statistics and asks them how much time they spend completing statistics homework each night. She would like to know if there is convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than 1 hour. The student plans to test the hypotheses, = 1 versus < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night. Assume all conditions have been met.

Question illustration
A
0.25
B
0.50
C
0.8
D
0.99
10

The owner of a fitness watch would like to determine if the mean number of steps he takes per day differs from the recommended 10,000 steps per day, using α = 0.05. He selects a random sample of 50 days with the intention of testing the hypotheses = 10,000 steps versus steps where μ = the true mean number of steps taken per day.Rather than test these hypotheses, he computes a 95% confidence interval for the true mean number of steps he takes per day. The 95% confidence interval is (8,250, 10,700). Based on the confidence interval, what conclusion can be made?

Question illustration
A
Reject H0. Since 10,000 does not fall outside the 95% confidence interval, there is convincing evidence that the true mean number of steps he takes per day differs from 10,000 steps.
B
Reject H0. Since 10,000 does not fall outside the 95% confidence interval, there is not convincing evidence that the true mean number of steps he takes per day differs from 10,000 steps.
C
Fail to reject H0. Since 10,000 does not fall outside the 95% confidence interval, there is convincing evidence that the true mean number of steps he takes per day differs from 10,000 steps.
D
Fail to reject H0. Since 10,000 does not fall outside the 95% confidence interval, there is not convincing evidence that the true mean number of steps he takes per day differs from 10,000 steps.

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