ISDS Exam 2 Terms
The ___________ hypothesis typically corresponds to a presumed default state of nature.
null
In a ______-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a ______-tailed test this region is located under both tails
one; two
The critical value approach specifies a region of values, also called the ________ region.
rejection
A __________ error is committed when we reject the null hypothesis, which is actually true
Type I
The _______ value approach specifies a region of values such that if the value of the test statistic falls into this region, then we reject the null hypothesis.
Critical
True or False: The critical value approach specifies a range of values, also called the rejection region, such that if the value of the test statistic falls into this range, we do not reject the null hypothesis.
False
The hypothesis statement H: µ = 25 is an example of a(an) ________ hypothesis.
Null
We define the allowed probability of making a Type I error as α, and we refer to 100α% as the ____________.
Significance Level
To obtain the p-value for a right-tailed test of the population mean, when σ is unknown, we use the Excel's function _________.
T.DIST.RT
Excel's function _______ returns the p-value for a right-tailed test.
Z.TEST
In general, the null and alternative hypotheses are __________. A. additive B. correlated C. multiplicative D. mutually exclusive
d
The _______________ approach specifies a range of values, also called the rejection region, such that if the value of the test statistic falls into this range, we reject the null hypothesis.
critical value
When conducting a hypothesis test for a given sample size, if a is increased from 0.05 to 0.10, then __________________. A. the probability of incorrectly rejecting the null hypothesis increases B. the probability of incorrectly failing to reject the null hypothesis decreases C. the probability of Type II error decreases D. All of the above
d
On the basis of sample information, we either ________ or ________ the null hypothesis
Reject or do not reject
True or False: For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error.
True
A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, Ho:μ ≥ 6 and HA:μ < 6, μ stand for _____________. A. the mean delivery time B. the standard deviation of the delivery time C. the number of deliveries that took less than 6 hours D. the proportion of deliveries that took less than 6 hours
a
As a general guideline, we use the __________________ hypothesis as a vehicle to establish something new, or contest the status quo, for which a corrective action may be required
alternative
The __________ hypothesis contradicts the default state of nature or status quo.
alternative
Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type II error is often referred to as ___________. A. a false positive B. a false negative C. a negative result D. the power of the test
b
Consider the following competing hypotheses: Ho:μ = 0, HA:μ ≠ 0. The value of the test statistic is z = −1.38. If we choose a 5% significance level, then we ___________________________________________. A. reject the null hypothesis and conclude that the population mean is significantly different from zero B. reject the null hypothesis and conclude that the population mean is not significantly different from zero C. do not reject the null hypothesis and conclude that the population mean is significantly different from zero D. do not reject the null hypothesis and conclude that the population mean is not significantly different from zero
d
Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim. A. H0:p = 0.84 and HA:p ≠ 0.84 B. H0:p < 0.84 and HA:p ≥ 0.84 C. H0:p ≤ 0.84 and HA:p > 0.84 D. H0:p ≥ 0.84 and HA:p < 0.84
d
True or False: A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean
True
A ________ error is made when we do not reject the null hypothesis that is actually false
Type II
A Type I error occurs when we ___________. A. reject the null hypothesis when it is actually true B. reject the null hypothesis when it is actually false C. do not reject the null hypothesis when it is actually true D. do not reject the null hypothesis when it is actually false
a
A hypothesis test regarding the population mean is based on ________________________________. A. the sampling distribution of the sample mean B. the sampling distribution of the sample variance C. the sampling distribution of the sample proportion D. the sampling distribution of the sample standard deviation
a
Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type I error is often referred to as ___________. A. a false positive B. a false negative C. a negative result D. the power of the test
a
Given the _________ of the z distribution, the p-value for a two-tailed test is twice that of the p-value for a one-tailed test
symmetry
The hypothesis statement H: < 60 is an example of a(an) ________ hypothesis
Alternative
True or False: Under the assumption that the null hypothesis is true as an equality, the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample.
True
A(n) ______ error is committed when we reject the null hypothesis when the null hypothesis is true.
Type 1
If the chosen significance level is α = 0.05, then ____________________________________________. A. there is a 5% probability of rejecting a true null hypothesis B. there is a 5% probability of accepting a true null hypothesis C. there is a 5% probability of rejecting a false null hypothesis D. there is a 5% probability of accepting a false null hypothesis
a
If the null hypothesis is rejected at a 1% significance level, then _____________. A. the null hypothesis will be rejected at a 5% significance level B. the alternative hypothesis will be rejected at a 5% significance level C. the null hypothesis will not be rejected at a 5% significance level D. the alternative hypothesis will not be rejected at a 5% significance level
a
A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________. A. the franchiser builds on an acceptable site B. the franchiser builds on an unacceptable site C. the franchiser does not build on an acceptable site D. the franchiser does not build on an unacceptable site
b
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The parameter to be tested is ___________________________. A. the mean GPA of all university students B. the mean GPA of the university honors students C. the mean GPA of 3.60 for the 36 selected honors students D. the proportion of honors students with a GPA exceeding 3.50
b
If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α =0.05, then the correct conclusion is to ____________________. A. reject the null hypothesis B. not reject the null hypothesis C. reject the null hypothesis if σ = 10 D. not reject the null hypothesis if σ = 10
b
What is the decision rule when using the p-value approach to hypothesis testing? A. Reject Ho if the p-value > α. B. Reject Ho if the p-value < α. C. Do not reject Ho if the p-value < 1 - α. D. Do not reject Ho if the p-value > 1 - α.
b
A two-tailed hypothesis test of the population mean or population proportion has ________. A. only one critical value B. two critical values, both positive C. two critical values, both negative D. two critical values, one positive and one negative
d
Which of the following answers represents the objective of a hypothesis test? A. Rejecting the null hypothesis when it is true. B. Rejecting the null hypothesis when it is false. C. Not rejecting the null hypothesis when it is true. D. Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true.
d
A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. If the advisor tests the hypotheses Ho: μ ≤ 300 versus HA: μ > 300, μ stands for ____________. A. the average number of automobiles that pass the intersection per hour B. the number of automobiles that pass the intersection per hour C. the proportion of automobiles that pass the intersection per hour D. the standard deviation of the number of automobiles that pass the intersection per hour
a
A one-tailed hypothesis test of the population mean has ______________. A. only one critical value B. two critical values, both positive C. two critical values, both negative D. two critical values, one positive and one negative
a
A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids." A. Type I: 4%, Type II: 6% B. Type I: 6%, Type II: 4% C. Type I: 94%, Type II: 4% D. Type I: 4%, Type II: 94%
a
A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of all students, and even a video recording of the exam in case additional evidence needs to be collected. He estimates that he catches 95% of students who cheat in his class, but 1% of the time that he accuses a student of cheating he is actually incorrect. Consider the null hypothesis, "the student is not cheating." What is the probability of a Type I error? A. 1% B. 5% C. 95% D. 99%
a
For a given sample size n, A. decreasing the probability of a Type I error α will increase the probability of a Type II error β B. decreasing the probability of a Type I error α will decrease the probability of a Type II error β C. changing the probability of a Type I error α will have no impact on the probability of a Type II error β D. increasing the probability of a Type I error α will increase the probability of a Type II error β as long as σ is known
a
If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________________. A. reject the null hypothesis B. not reject the null hypothesis C. reject the null hypothesis if σ = 10 D. not reject the null hypothesis if σ = 10
a
It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. In testing the politician's claim, how does one define the population parameter of interest? A. The current proportion of babies born out of wedlock B. The mean number of babies born out of wedlock C. The number of babies born out of wedlock D. The general belief that the proportion of babies born out of wedlock is no more than 0.50
a
It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. When testing the two hypotheses, H0: p ≤ 0.50 and HA: p > 0.50, p stands for _____________. A. the current proportion of babies born out of wedlock B. the mean number of babies born out of wedlock C. the number of babies born out of wedlock D. the general belief that the proportion of babies born out of wedlock is no more than 0.50
a
The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest? A. The mean score on the eighth-grade reading comprehension test B. The number of eighth graders who took the reading comprehension test C. The standard deviation of the score on the eighth-grade reading comprehension test D. The proportion of eighth graders who scored above 73 on the reading comprehension test
a
When conducting a hypothesis test, which of the following decisions represents an error? A. Rejecting the null hypothesis when it is true. B. Rejecting the null hypothesis when it is false. C. Not rejecting the null hypothesis when it is true. D. Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true.
a
When we reject the null hypothesis when it is actually false, we have committed _________. A. no error B. a Type I error C. a Type II error D. a Type I error and a Type II error
a
It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. Identify the correct null and alternative hypotheses to test the politician's claim. A. H0:p = 0.50 and HA:p ≠ 0.50 B. H0:p ≤ 0.50 and HA:p > 0.50 C. H0:p ≥ 0.50 and HA:p > 0.50 D. H0:p ≥ 0.50 and HA:p < 0.50
b
The alternative hypothesis typically ___________. A. corresponds to the presumed default state of nature B. contests the status quo, for which a corrective action may be required C. states the probability of rejecting the null hypothesis when it is false D. states the probability of rejecting the null hypothesis when it is true
b
Which of the following are two-tailed tests? A. Ho:μ ≤ 10, HA:μ > 10 B. Ho:μ = 10, HA:μ ≠ 10 C. Ho:μ ≥ 400, HA:μ < 400 D. Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400
b
When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the ______________________________________. A. probability of Type II error decreases B. probability of incorrectly rejecting the null hypothesis increases C. probability of incorrectly accepting the null hypothesis increases D. probability of incorrectly accepting the null hypothesis decreases
c
Which of the following are one-tailed tests? A. Ho:μ ≤ 10, HA:μ > 10 B. Ho:μ = 10, HA:μ ≠ 10 C. Ho:μ ≥ 400, HA:μ < 400 D. Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400
d
Which of the following types of tests may be performed? A. Right-tailed and two-tailed tests B. Left-tailed and two-tailed tests C. Right-tailed and left-tailed tests D. Right-tailed, left-tailed, and two-tailed tests
d
The null hypothesis in a hypothesis test refers to _____________. A. the desired outcome B. the default state of nature C. the altered state of nature D. the desired state of nature
B
If we reject a null hypothesis at the 1% significance level, then we have _________ evidence that the null hypothesis is false.
Very strong
A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that__________________________. A. the franchiser builds on an acceptable site B. the franchiser builds on an unacceptable site C. the franchiser does not build on an acceptable site D. the franchiser does not build on an unacceptable site
c
