Question 1

A candidate for state representative of a certain state claims to be favored by at least half of the voters. If ahypothesis test is performed, how should you interpret a decision that rejects the null hypothesis? 
A) There is sufficient evidence to reject the claim $\mathrm { p } \geq 0.5$.
B) There is not sufficient evidence to reject the claim $p \geq 0.5$.
C) There is sufficient evidence to support the claim $p \geq 0.5$.
D) There is not sufficient evidence to support the claim $p \geq 0.5$.

Accepted Answer

Rejecting the null hypothesis means there is sufficient evidence to reject the claim that the proportion of voters favoring the candidate is at least 0.5.

Question 2

A candidate for state representative of a certain state claims to be favored by at least half of the voters. If ahypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis? 
A) There is not sufficient evidence to reject the claim $\mathrm { p } \geq 0.5$.
B) There is sufficient evidence to reject the claim $p \geq 0.5$.
C) There is sufficient evidence to support the claim $p \geq 0.5$.
D) There is not sufficient evidence to support the claim $p \geq 0.5$. 10.2 Hypothesis Tests for a Population Proportion1 Explain the logic of hypothesis testing.

Accepted Answer

Failing to reject the null hypothesis means there isn't enough evidence against it, not that the alternative hypothesis is proven.

Question 3

The mean age of judges in Dallas is greater than  50.2  years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?
A) There is not sufficient evidence to support the claim $\mu > 50.2$
B) There is sufficient evidence to reject the claim $\mu > 50.2$
C) There is not sufficient evidence to reject the claim $\mu > 50.2$
D) There is sufficient evidence to support the claim $u > 50.2$

Accepted Answer

Failing to reject the null hypothesis means there isn't enough evidence to support the alternative hypothesis, which in this case is that the mean age is greater than 50.2 years.

Question 4

Suppose you want to test the claim that $\mu = 3.5 .$ Given a sample size of n=48 and a level of significance of $\alpha$=0.01 , when should you reject H₀ ? A) Reject H₀ if the standardized test statistic is greater than 2.575 or less than -2.575 . B) Reject H₀ if the standardized test statistic is greater than 2.33 or less than -2.33 . C) Reject H₀ if the standardized test statistic is greater than 1.96 or less than -1.96 D) Reject H₀ if the standardized test statistic is greater than 1.645 or less than -1.645

Accepted Answer

The correct rejection rule at a significance level of $\alpha = 0.01$ for a two-tailed test is to reject the null hypothesis if the standardized test statistic is greater than the critical value or less than the negative of the critical value associated with $\alpha = 0.01$. The critical values for a two-tailed test at this significance level are typically around ±2.575, which corresponds to the critical values for the 99% confidence level (or the 1% significance level in a two-tailed test).

Question 5

The mean age of professors at a university is greater than  58.3  years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
A) There is sufficient evidence to support the claim $\mu > 58.3 .$
B) There is sufficient evidence to reject the claim $\mu > 58.3 .$
C) There is not sufficient evidence to reject the claim $\mu > 58.3$
D) There is not sufficient evidence to support the claim $\mu > 58.3$

Accepted Answer

Rejecting the null hypothesis in this context means that the data provides sufficient evidence to support the alternative hypothesis, which is that the mean age of professors is greater than 58.3 years.

Question 6

The mean monthly gasoline bill for one household is greater than $150. If a hupothesis test is performed, how should you interpret a dicision that fails to reject the null hypothesis?
A) There is  sufficient evidence to support the claim $$\mu > \$ 150$$
B) There is sufficient evidence to reject the claim $$\mu > \$ 150$$
C) There is not sufficient evidence to reject the claim $$\mu > \$ 150$$
D) There is not sufficient evidence to support  the claim $$\mu > \$ 150$$

Accepted Answer

The answer of The mean monthly gasoline bill for one...

Question 7

Find the critical value for a left-tailed test with α = 0.025.
A) -1.96
B) -2.24
C) -1.645
D) -2.575

Accepted Answer

For a left-tailed test with α = 0.025, the critical value corresponds to the z-score that has 2.5% of the distribution to its left. This value is -1.96.

Question 8

The dean of a major university claims that the mean number of hours students study at her University (perday) is at most 3.6 hours. If a hypothesis test is performed, how should you interpret a decision that rejects thenull hypothesis? 
A) There is sufficient evidence to reject the claim $\mu \leq 3.6$.
B) There is not sufficient evidence to reject the claim $\mu \leq 3.6$.
C) There is sufficient evidence to support the claim $\mu \leq 3.6$.
D) There is not sufficient evidence to support the claim $\mu \leq 3.6$.

Accepted Answer

Rejecting the null hypothesis means the data provides sufficient evidence to conclude that the mean number of hours students study per day is more than 3.6 hours, contradicting the dean's claim.

Question 9

The mean age of principals in a local school district is  50.2  years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
A) There is sufficient evidence to reject the claim $\mu = 50.2$
B) There is not sufficient evidence to reject the claim $\mu = 50.2$
C) There is sufficient evidence to support the claim $\mu = 50.2$
D) There is not sufficient evidence to support the claim $\mu = 50.2$

Accepted Answer

Rejecting the null hypothesis means there is sufficient evidence to conclude that the mean age of principals is not 50.2 years, thus rejecting the claim $\mu = 50.2$.

Question 10

The mean monthly gasoline bill for one household is greater than $160. If a hupothesis test is performed, how should you interpret a dicision that fails to reject the null hypothesis?
A) There is not sufficient evidence to support the claim $$\mu > \$ 160$$
B) There is sufficient evidence to reject the claim $$\mu > \$ 160$$
C) There is not sufficient evidence to reject the claim $$\mu > \$ 160$$
D) There is sufficient evidence to support  the claim $$\mu > \$ 160$$

Accepted Answer

Failing to reject the null hypothesis means there isn't enough evidence to support the alternative hypothesis, which in this case is that the mean monthly gasoline bill is greater than $160.

Question 11

If we do not reject the null hypothesis when the null hypothesis is in error, then we have made a
A) Type II error
B) Type I error
C) Correct decision
D) Type β error

Accepted Answer

A Type II error occurs when we fail to reject the null hypothesis even though it is false.

Question 12

Find the critical value for a two-tailed test with α = 0.08.
A) ±1.75
B) ±1.405
C) ±2.65
D) ±1.96

Accepted Answer

The critical value for a two-tailed test with α = 0.08 (which means each tail has α/2 = 0.04) corresponds to the z-value that bounds the middle 92% of the standard normal distribution. The z-value closest to this description is ±1.75.

Question 13

The mean age of professors at a university is  57.9  years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?
A) There is not sufficient evidence to reject the claim $\mu = 57.9$
B) There is sufficient evidence to reject the claim $\mu = 57.9$
C) There is sufficient evidence to support the claim $\mu = 57.9$
D) There is not sufficient evidence to support the claim $\mu = 57.9$

Accepted Answer

Failing to reject the null hypothesis means there isn't enough evidence against the null hypothesis, which in this context is the claim that the mean age is 57.9 years.

Question 14

We never conclude "Accept H₀ " in a test of hypothesis. This is because: A) $\beta$=p (Type II error) is not known. B) $\alpha$ is the probability of a Type I error. C) The rejection region is not known. D) The p-value is not small enough.

Accepted Answer

In hypothesis testing, we never "accept" the null hypothesis (H0) because failing to reject H0 does not prove it true. The probability of a Type II error ($\beta$) is not known, which means we cannot determine the likelihood of incorrectly accepting H0.

Question 15

The mean number of rushing yards for one NFL team was less than 109 yards per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?
A) There is not sufficient evidence to support the claim $\mu < 109 .$
B) There is sufficient evidence to reject the claim $\mu < 109$
C) There is not sufficient evidence to reject the claim $\mu < 109$
D) There is sufficient evidence to support the claim $\mu < 109 .$

Accepted Answer

Failing to reject the null hypothesis means there isn't enough evidence to support the alternative hypothesis, which in this context is the claim that the mean number of rushing yards is less than 109 yards per game.

Question 16

If we reject the null hypothesis when the null hypothesis is true, then we have made a
A) Type I error
B) Type II error
C) Correct decision
D) Type α error

Accepted Answer

Rejecting the null hypothesis when it is actually true is defined as a Type I error.

Question 17

The dean of a major university claims that the mean number of hours students study at her University (perday) is at most 4.4 hours. If a hypothesis test is performed, how should you interpret a decision that fails toreject the null hypothesis? 
A) There is not sufficient evidence to reject the claim $\mu \leq 4.4$.
B) There is sufficient evidence to reject the claim $\mu \leq 4.4$.
C) There is sufficient evidence to support the claim $\mu \leq 4.4$.
D) There is not sufficient evidence to support the claim $\mu \leq 4.4$.

Accepted Answer

Failing to reject the null hypothesis means there isn't enough evidence against the null hypothesis, which in this case is the claim that the mean number of study hours per day is at most 4.4 hours.

Question 18

The mean number of rushing yards for one NFL team was less than 99 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
A) There is sufficient evidence to support the claim $\mu < 99 .$
B) There is sufficient evidence to reject the claim $\mu < 99 .$
C) There is not sufficient evidence to reject the claim $\mu < 99 .$
D) There is not sufficient evidence to support the claim $\mu < 99 .$

Accepted Answer

Rejecting the null hypothesis in this context means accepting the alternative hypothesis, which is the claim that the mean number of rushing yards per game is less than 99.

Question 19

The level of significance, α, is the probability of making a
A) Type I error
B) Type II error
C) Correct decision
D) Type β error

Accepted Answer

The level of significance, α, is the probability of making a Type I error, which occurs when a true null hypothesis is incorrectly rejected.

Question 20

True or False: Type I and Type II errors are independent events.

Accepted Answer

Type I and Type II errors are not independent because decreasing the probability of one increases the probability of the other, given a fixed amount of information.

Quiz 10: Hypothesis Tests Regarding a Parameter

A candidate for state representative of a certain state claims to be favored by at least half of the voters. If ahypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A candidate for state representative of a certain state claims to be favored by at least half of the voters. If ahypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

The mean age of judges in Dallas is greater than 50.2 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

Suppose you want to test the claim that $\mu = 3.5 .$ Given a sample size of n=48 and a level of significance of $\alpha$ =0.01 , when should you reject H₀ ?

The mean age of professors at a university is greater than 58.3 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

The mean monthly gasoline bill for one household is greater than $150. If a hupothesis test is performed, how should you interpret a dicision that fails to reject the null hypothesis?

Find the critical value for a left-tailed test with α = 0.025.

The dean of a major university claims that the mean number of hours students study at her University (perday) is at most 3.6 hours. If a hypothesis test is performed, how should you interpret a decision that rejects thenull hypothesis?

The mean age of principals in a local school district is 50.2 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

The mean monthly gasoline bill for one household is greater than $160. If a hupothesis test is performed, how should you interpret a dicision that fails to reject the null hypothesis?

If we do not reject the null hypothesis when the null hypothesis is in error, then we have made a

Find the critical value for a two-tailed test with α = 0.08.

The mean age of professors at a university is 57.9 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

We never conclude "Accept H₀ " in a test of hypothesis. This is because:

The mean number of rushing yards for one NFL team was less than 109 yards per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

If we reject the null hypothesis when the null hypothesis is true, then we have made a

The dean of a major university claims that the mean number of hours students study at her University (perday) is at most 4.4 hours. If a hypothesis test is performed, how should you interpret a decision that fails toreject the null hypothesis?

The mean number of rushing yards for one NFL team was less than 99 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

The level of significance, α, is the probability of making a

True or False: Type I and Type II errors are independent events.

Quiz 10: Hypothesis Tests Regarding a Parameter

A candidate for state representative of a certain state claims to be favored by at least half of the voters. If ahypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A candidate for state representative of a certain state claims to be favored by at least half of the voters. If ahypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

The mean age of judges in Dallas is greater than 50.2 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

Suppose you want to test the claim that μ=3.5.\mu = 3.5 .μ=3.5. Given a sample size of n=48 and a level of significance of α\alphaα =0.01 , when should you reject H0 ?

The mean age of professors at a university is greater than 58.3 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

The mean monthly gasoline bill for one household is greater than $150. If a hupothesis test is performed, how should you interpret a dicision that fails to reject the null hypothesis?

Find the critical value for a left-tailed test with α = 0.025.

The dean of a major university claims that the mean number of hours students study at her University (perday) is at most 3.6 hours. If a hypothesis test is performed, how should you interpret a decision that rejects thenull hypothesis?

The mean age of principals in a local school district is 50.2 years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

The mean monthly gasoline bill for one household is greater than $160. If a hupothesis test is performed, how should you interpret a dicision that fails to reject the null hypothesis?

If we do not reject the null hypothesis when the null hypothesis is in error, then we have made a

Find the critical value for a two-tailed test with α = 0.08.

The mean age of professors at a university is 57.9 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

We never conclude "Accept H0 " in a test of hypothesis. This is because:

The mean number of rushing yards for one NFL team was less than 109 yards per game. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

If we reject the null hypothesis when the null hypothesis is true, then we have made a

The dean of a major university claims that the mean number of hours students study at her University (perday) is at most 4.4 hours. If a hypothesis test is performed, how should you interpret a decision that fails toreject the null hypothesis?

The mean number of rushing yards for one NFL team was less than 99 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

The level of significance, α, is the probability of making a

True or False: Type I and Type II errors are independent events.

Suppose you want to test the claim that $\mu = 3.5 .$ Given a sample size of n=48 and a level of significance of $\alpha$ =0.01 , when should you reject H₀ ?

We never conclude "Accept H₀ " in a test of hypothesis. This is because: