Chapter 10
We wish to test H0: μ ≤ 12 and H1: μ > 12 at the 0.05 level of significance. Which of these statements are correct? Select all that apply.
Fail to reject H0 if z < 1.65 Reject H0 if z > 1.65
We wish to test H0: μ ≥ 30 and H1: μ < 30 at the 0.05 level of significance. Which of these statements are correct? Select all that apply.
Fail to reject H0 if z > -1.65 Reject H0 if z < -1.65
A bag of potatoes has a stated weight of 10 pounds with σ = 0.75 pound. A sample of 30 bags has an average weight of 10.3 pounds. Conduct a hypothesis test using a 1% significance level for: H0: μ = 10 H1: μ ≠ 10Fa
Fail to reject the null hypothesis
If the test statistic for a hypothesis test (H0: μ = 11) is z = 1.82 and the critical value for 5% significance is zc = 1.96, what should our conclusion be?
Fail to reject the null hypothesis.
The null hypothesis is not rejected if the confidence interval does not include the hypothesized value.
False
What is the correct procedure when you want to do a test of the population mean but the population standard deviation is unknown? Select all that apply.
Find the sample standard deviation and use it as an estimate for the population standard deviation. The t-distribution is used in place of the z-distribution, assuming a normal population.
Which one of the following sets of hypotheses requires the use of a two-tailed test?
H0: μ = 5.6, H1: μ ≠ 5.6
Which of the following sets of hypotheses require the use of a one-tailed test? Select all that apply.
H0: μ ≤ -25, H1: μ > -25 H0: μ ≥ 7.5, H1: μ < 7.5
Which of the following statements of a test hypothesis uses the correct protocol for stating an alternate hypothesis?
H1: μ ≠ 24 H1: μ < 30
Which of the following statements of a test hypothesis violates the protocol for choosing null and alternate hypotheses?
H1: μ ≤ -2
Which of the following statements accurately describe the p-value? Select all that apply.
If we reject the null, it is the probability of making a Type I error. The null is rejected when the p-value is less than α.
What is the last step in the six step Hypothesis testing procedure?
Interpret the result.
Which of the following is the best definition of the null hypothesis?
It is a statement that is not rejected unless the sample data provide convincing evidence that it is false.
Which of the following is a "hypothesis" in the statistical sense? Select all that apply.
The population mean lifetime of a particular brand of light bulb is at least 1000 hours. The population mean miles per gallon of a particular car is 44.
When testing a mean, where the population standard deviation is known, we calculate the test statistic using the formula z = X−μσ/n√X-μσ/n. Match the variables to their description.
z matches Choice The test statistic XX matches Choice The Sample mean μ matches Choice The population mean σ/n⎯⎯√n matches Choice The Standard error
The probability of rejecting a true null is know as which of the following? Select all that apply.
α Type I error
Which of the following statements accurately describe the alternate hypothesis? Select all that apply.
It is accepted as a consequence of the null hypothesis being rejected. It is also called the "research hypothesis".
The result of a hypothesis test was traditionally reported as either "reject H0" or "fail to reject H0". What is the purpose of reporting the p-value in addition?
It provides additional insight into the strength of the decision.
Which of the following statements are valid descriptions of the alternate hypothesis? Select all that apply.
It tells what you will conclude if you reject the null hypothesis. It is written symbolically as H1.
What is the "critical value" for a hypothesis test?
The dividing point between rejecting and failing to reject the null hypothesis.
Which of the following best summarizes the process of selecting a significance level for a hypothesis test of the mean?
The investigator should select the significance level before setting up the decision rule and taking the sample data.
A tire manufacturer claims its new tire has an average tread life of 80,000. To test to see if the process is true, the company conducts a hypothesis test using the following hypotheses: Ho: μ=80,000 H1: μ≠80,000 If the null is rejected, what would the interpretation be?
The manufacturer's claim is not true - the population average is not 80,000
What is the meaning of "level of significance" in the context of hypothesis testing?
The probability of rejecting the null hypothesis when it is true.
Calculate the test statistic z for a population mean of 30, a population standard deviation of 6, a sample mean of 27 and a sample size of 20.
-2.24
Find the p-value (to two significant digits) for the following test. H0: μ = 0, H1: μ ≠ 0, σ = 1, z = 2.06 Hint: the population follows the standard normal distribution.
0.04
Match the level of significance to the type of research for which it is traditionally chosen.
0.05 matches Choice consumer research 0.01 matches Choice quality assurance 0.10 matches Choice political polling
Calculate the test statistic z for a population mean of 5.5, a population standard deviation of 2, a sample mean of 6.7 and a sample size of 10.
1.90
Suppose a hypothesis test, using α = 0.05, is being conducted with the following null hypothesis: H0: μ = 2. Which one of the following confidence intervals would lead to rejecting the null hypothesis?
A 95% confidence interval of 3 to 4.
Which one of the following best describes Hypothesis Testing?
A procedure based on sample evidence and probability to see if a hypothesis is a reasonable statement.
Choose the best definition of "hypothesis" in the context of statistical analysis.
A statement about a population parameter subject to verification.
How does the use of a two-tailed test effect the size of the rejection area?
Because there are two tails and the total significance remains the same, the area in each tail is half as much.
Which symbol represents the level of significance?
a
A tire manufacturer claims its new tire has an average tread life of 80,000. To test to see if the process is true, the company conducts a hypothesis test using the following hypotheses: Ho: μ=80,000 H1: μ≠80,000 Which of the following is the result of a Type II error?
Concluding the population average is 80,000 when it really isn't.
A soda bottling company fills bottles with 12 ounces of soda. Overfilling causes the company to give away free soda. Underfilling causes the company to cheat the customer. To test to see if the process is working correctly, the company conducts a hypothesis test using the following hypotheses: Ho: μ=12 H1: μ≠12 Which of the following is the result of a Type I error?
Concluding the population average is not 12 when it really is.
A brand of chocolate bar has a stated weight of 6 oz. with σ = 0.25 oz. A sample of 9 bars has an average weight of 6.05 oz. Test H0: μ = 6 oz. H1: μ ≠6 oz. at the 5% significance level.
Do not reject the null hypothesis
Which of the following are essential elements of hypothesis testing? Select all that apply.
It uses probability theory to determine if a hypothesis is a reasonable statement. It makes use of sample data.
If we reject a false null hypothesis, what type of error would we be making?
No error was made
Choose the statements that correctly reflect traditional usage of significance level in statistical research. Select all that apply.
Quality control uses a 1% significance level. Consumer research uses a 5% significance.
Suppose you are performing a hypothesis test with σ unknown, n=29, α=0.01, and the following hypotheses: H0: μ ≤ 24 H1: μ > 24 What is the decision rule?
Reject H0 if the test statistic is greater than 2.467.
Suppose you are performing a hypothesis test with σ unknown, n = 23, α = 0.10, and the following hypotheses: H0: μ ≥ 24 H1: μ < 24 What is the decision rule?
Reject H0 if the test statistic is less than −1.321.
A model of car claims mileage of 24 mpg. with σ = 4 mpg. A sample of 4 cars got an average of 20.5 mpg. Test H0: μ = 24 H1: μ ≠ 24 at the 10% significance level.
Reject the null hypothesis
If the test statistic for a hypothesis test (H0: μ = 25) is z = 2.05 and the critical value for 5% significance is 1.96, what should our conclusion be?
Reject the null hypothesis and conclude the alternative is true.
What is a "decision rule" in the context of hypothesis testing?
The specific conditions under which the null hypothesis is to be rejected.
From the statements below, select all that are accurate descriptions of the null hypothesis.
The term "null" refers to no significant difference. The purpose of the test is to prove the null hypothesis is false. The null hypothesis is designated H0.
A soda bottling company fills bottles with 12 ounces of soda. Overfilling causes the company to give away free soda. Underfilling causes the company to cheat the customer. To test to see if the process is working correctly, the company conducts a hypothesis test using the following hypotheses: Ho: μ=12 H1: μ≠12 If we fail to reject the null, what would the interpretation be?
There is insufficient evidence to conclude that the mean is different from 12.