Chapter 10 Flashcards
(21 cards)
The _______ _______ is a statement of no change comma no effect comma or no difference.
Null Hypothesis
10.1 The Language of Hypotheis Test
If we reject the null hypothesis when the statement in the null hypothesis is true, we have made a Type _______ error.
Type I Error
If a hypothesis is tested at the α=0.05 level of significance, what is the probability of making a type I error?
Choose the correct answer below.
A.
The probability of making a type I error is 0.95.
B.
The probability of making a type I error is 0.05.
C.
The probability of making a type I error is 0.5.
D.
There is insufficient information to determine the probability of a type I error.
B.
The probability of making a type I error is 0.05.
Determine whether the following statement is true or false.
Sample evidence can prove that a null hypothesis is true.
Choose the correct answer below.
False
True
False
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested?
Upper H 0:
p
equals
0.4
Upper H1:
p
less than
0.4
What type of test is being conducted in this problem?
Right-tailed test
Two-tailed test
Left-tailed test
What parameter is being tested?
Population mean
Population standard deviation
Population proportion
Left-tailed, population proportion
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested?
Upper H 0: sigma equals 4.2
Upper H 1: sigma not equals 4.2
Choose the correct answer below.
Left dash tailed
Two dash tailed
Right dash tailed
What parameter is being tested?
mu
p
sigma
Two-tailed, sigma
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested?
Upper H 0:
mu
equals
110
Upper H 1:
mu
not equals
110
Is the hypothesis test left-tailed, right-tailed, or two-tailed?
Left-tailed test
Right-tailed test
Two-tailed test
What parameter is being tested?
Population standard deviation
Population mean
Population proportion
Two-tailed, population mean
Suppose the null hypothesis is rejected. State the conclusion based on the results of the test.
Three years ago, the mean price of a single-family home was $243 comma 735. A real estate broker believes that the mean price has increased since then.
Which of the following is the correct conclusion?
A.
There is sufficient evidence to conclude that the mean price of a single-family home has not changed.
B.
There is not sufficient evidence to conclude that the mean price of a single-family home has not changed.
C.
There is sufficient evidence to conclude that the mean price of a single-family home has increased.
D.
There is not sufficient evidence to conclude that the mean price of a single-family home has increased.
C.
There is sufficient evidence to conclude that the mean price of a single-family home has increased.
State the conclusion based on the results of the test.
The mean of the pressure required to open a certain valve is known to be mu equals 6.8 psi. Due to changes in the manufacturing process, the quality-control manager feels that the average pressure has increased. The null hypothesis was rejected.
Choose the correct answer below.
A.
There is not sufficient evidence that the mean of the pressure required to open a certain valve has increased.
B.
There is sufficient evidence that the mean of the pressure required to open a certain valve has not changed.
C.
The mean of the pressure has increased.
D.
The mean of the pressure has not changed.
E.
There is not sufficient evidence that the mean of the pressure required to open a certain valve has not changed.
F.
There is sufficient evidence that the mean of the pressure required to open a certain valve has increased.
F.
There is sufficient evidence that the mean of the pressure required to open a certain valve has increased.
State the conclusion based on the results of the test.
According to the report, the standard deviation of monthly cell phone bills was $48.15 three years ago. A researcher suspects that the standard deviation of monthly cell phone bills is higher today. The null hypothesis is rejected.
Choose the correct answer below.
A.
There is sufficient evidence to conclude that the standard deviation of monthly cell phone bills is higher than its level three years ago of $48.15.
B.
There is sufficient evidence to conclude that the standard deviation of monthly cell phone bills is less than its level three years ago of $48.15.
C.
There is not sufficient evidence to conclude that the standard deviation of monthly cell phone bills is higher than its level three years ago of $48.15.
A.
There is sufficient evidence to conclude that the standard deviation of monthly cell phone bills is higher than its level three years ago of $48.15.
State the conclusion based on the results of the test.
According to the Federal Housing Finance Board, the mean price of a single-family home two years ago was $299 comma 700. A real estate broker believes that because of the recent credit crunch, the mean price has increased since then. The null hypothesis is not rejected.
Choose the correct answer below.
A.
There is sufficient evidence to conclude that the mean price of a single-family home has decreased from its level two years ago of $299 comma 700.
B.
There is sufficient evidence to conclude that the mean price of a single-family home has increased from its level two years ago of $299 comma 700.
C.
There is not sufficient evidence to conclude that the mean price of a single-family home has increased from its level two years ago of $299 comma 700.
D.
There is not sufficient evidence to conclude that the mean price of a single-family home has decreased from its level two years ago of $299 comma 700.
C.
There is not sufficient evidence to conclude that the mean price of a single-family home has increased from its level two years ago of $299 comma 700.
Question content area top
Part 1
If the consequences of making a Type I error are severe, would you choose the level of significance, alpha, to equal 0.01, 0.05, or 0.10?
Question content area bottom
Part 1
Choose the correct answer below.
A.
0.01
B.
0.05
C.
0.10
A.
0.01
What happens to the probability of making a Type II error, beta, as the level of significance, alpha, decreases? Why?
Choose the correct answer below
A.
The probability increases. The sum of alpha and beta always equals 1.
B.
The probability increases. Type I and Type II errors are inversely related.
C.
The probability decreases. Type I and Type II errors are proportional.
D.
The probability decreases. The more careful researcher is, the lower the chances of making any error.
B.
The probability increases. Type I and Type II errors are inversely related.
What is at the “heart” of hypothesis testing in statistics?
Choose the best answer below.
A.
Make an assumption about reality, and collect sample evidence to determine whether it contradicts the assumption.
B.
Determine whether a statement is true.
C.
Determine whether a statement is false.
D.
None of the above
A.
Make an assumption about reality, and collect sample evidence to determine whether it contradicts the assumption.
The
______
hypothesis, denoted Upper H 0, is a statement to be tested, and is a statement of no change, no effect, or no difference.
null
The
________
hypothesis, denoted Upper H 1, is a statement that the researcher is trying to find evidence to support.
alternative
If Upper H 0: parameterequalssome value and Upper H 1: parametergreater thansome value, the hypothesis test is a ____
-tailed test.
Right
Question content area top
Part 1
For students who first enrolled in two year public institutions in a recent semester, the proportion who earned a bachelor’s degree within six years was 0.388. The president of a certain college believes that the proportion of students who enroll in her institution have a lower completion rate.
(a)
Determine the null and alternative hypotheses.
(b)
Explain what it would mean to make a Type I error.
(c)
Explain what it would mean to make a Type II error.
(a) State the hypotheses.
(b) Which of the following is a Type I error?
A.
The president rejects the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is 0.388.
B.
The president fails to reject the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is 0.388.
C.
The president rejects the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is less than 0.388.
D.
The president fails to reject the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is less than 0.388.
(c) Which of the following is a Type II error?
A.
The president fails to reject the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is 0.388.
B.
The president rejects the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is 0.388.
C.
The president rejects the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is less than 0.388.
D.
The president fails to reject the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is less than 0.388.
(b) A.
The president rejects the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is 0.388. (c) D.
The president fails to reject the hypothesis that the proportion of students who earn a bachelor’s degree within six years is 0.388, when, in fact, the proportion is less than 0.388.
Three years ago, the mean price of an existing single-family home was $243 comma 716. A real estate broker believes that existing home prices in her neighborhood are lower.
(a)
Determine the null and alternative hypotheses.
(b)
Explain what it would mean to make a Type I error.
(c)
Explain what it would mean to make a Type II error.
(a) State the hypotheses.
Upper H 0:
mu
equals
$
243,716
Upper H 1:
mu
less than
$
243,716
(Type integers or decimals. Do not round.)
Part 2
(b) Which of the following is a Type I error?
A.
The broker rejects the hypothesis that the mean price is $243 comma 716, when the true mean price is less than $243 comma 716.
B.
The broker fails to reject the hypothesis that the mean price is $243 comma 716, when it is the true mean cost.
C.
The broker fails to reject the hypothesis that the mean price is $243 comma 716, when the true mean price is less than $243 comma 716.
D.
The broker rejects the hypothesis that the mean price is $243 comma 716, when it is the true mean cost.
Your answer is correct.
Part 3
(c) Which of the following is a Type II error?
A.
The broker rejects the hypothesis that the mean price is $243 comma 716, when it is the true mean cost.
B.
The broker rejects the hypothesis that the mean price is $243 comma 716, when the true mean price is less than $243 comma 716.
C.
The broker fails to reject the hypothesis that the mean price is $243 comma 716, when the true mean price is less than $243 comma 716.
D.
The broker fails to reject the hypothesis that the mean price is $243 comma 716, when it is the true mean cost.
(b)D, (c)C
Suppose the null hypothesis is not rejected. State the conclusion based on the results of the test.
Six years ago, 12.7% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then.
Which of the following is the correct conclusion?
A.
There is not sufficient evidence to conclude that the percentage of teenage mothers has decreased.
B.
There is sufficient evidence to conclude that the percentage of teenage mothers has decreased.
C.
There is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
D.
There is sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
A.
There is not sufficient evidence to conclude that the percentage of teenage mothers has decreased.
Question content area top
Part 1
Suppose the null hypothesis is not rejected. State the conclusion based on the results of the test.
Six years ago, 11.1% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then.
hich of the following is the correct conclusion?
A.
There is sufficient evidence to conclude that the percentage of teenage mothers has decreased.
B.
There is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
C.
There is sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
D.
There is not sufficient evidence to conclude that the percentage of teenage mothers has decreased.
D.
There is not sufficient evidence to conclude that the percentage of teenage mothers has decreased.
