Question 1

In order to make statistical inferences about σ² that are valid using a chi-square distribution,the assumption is that the sampled population is also a chi-square distribution.

Accepted Answer

The assumption is that the sampled population is a normal distribution.

Question 2

A null hypothesis is not rejected at a given level of significance.As the assumed value of the mean gets further away from the true population mean,the type II error will _____________.
A)Increase
B)Decrease
C)Stay the same
D)Randomly fluctuate

Accepted Answer

The answer of A null hypothesis is not rejected at...

Question 3

The ____________ hypothesis will be accepted only if there is convincing sample evidence that it is true.
A)z test
B)Alternative
C)Null
D)True

Accepted Answer

The answer of The ____________ hypothesis will be accepted only...

Question 4

χ²_α is the point on the vertical axis under the curve of the chi-square distribution that gives a right-hand tail area equal to α.

Accepted Answer

It is the point on the horizontal axis.

Question 5

For a fixed sample size,the lower we set α,the higher is the ___________.
A)Type I error
B)Type II error
C)Random error
D)p-value

Accepted Answer

The answer of For a fixed sample size,the lower we...

Question 6

The rejection of a true null hypothesis is called a ______________ error.
A)Type I
B)Type II
C)Random
D)β

Accepted Answer

A rejection of a true null hypothesis is called a Type I error. This means that a researcher has incorrectly rejected a hypothesis that is actually true. Type II errors, on the other hand, occur when a researcher fails to reject a false null hypothesis. Random and β do not relate to this specific type of error.

Question 7

When evaluating a new process,using the square root of the upper end of the confidence interval for σ² gives an estimate of the smallest that σ for the new process might reasonably be.

Accepted Answer

Gives an estimate of the largest that σ might reasonably be.

Question 8

The ____________ hypothesis is not rejected unless there is sufficient sample evidence to do so.
A)Research
B)Alternative
C)Null
D)True

Accepted Answer

The null hypothesis is the hypothesis which is assumed to be true until there is sufficient sample evidence to reject it. Therefore, it is not rejected unless there is enough evidence to do so. The alternative hypothesis is the opposite of the null hypothesis and is only accepted if the null hypothesis is rejected. The research hypothesis is a broader hypothesis used to frame the research question and is not directly related to hypothesis testing. The true hypothesis is not a valid option as it is not a common type of hypothesis used in statistical analysis.

Question 9

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.Identify the null hypothesis.
A)p ≠ .66
B)p> .66
C)p ≤ .66

Accepted Answer

Since we want to prove that the proportion of citizens supporting an increase in cigarette taxes is greater than 0.66, we take the complement of that for the null.

Question 10

The value of the test statistic is compared with a(n)_______________ in order to decide whether the null hypothesis can be rejected.
A)α
B)β
C)p-value
D)critical value

Accepted Answer

The critical value is the predetermined value that sets the threshold for rejecting the null hypothesis. The test statistic is compared with this critical value to determine if it falls within the appropriate range for rejecting the null hypothesis at a certain level of significance (e.g., α = 0.05). The other options are related to hypothesis testing but do not directly involve comparing the test statistic to a predetermined value. α is the significance level chosen by the researcher, β is the probability of a Type II error, and the p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.

Question 11

Assuming a fixed sample size,as α (Type I error)decreases,β (Type II error)___________.
A)Increases
B)Decreases
C)Stays the same
D)Randomly fluctuates

Accepted Answer

As the significance level (α) decreases, it becomes less likely to reject the null hypothesis, which increases the chances of making a Type II error. Therefore, the power of the test, which is (1-β), decreases, and β increases.

Question 12

When testing a hypothesis about a single mean,if the sample size is 20,the population standard deviation is unknown,and the population is assumed to be a normal distribution,the correct test statistic to use is ___________.
A)r
B)z
C)t
D)p-value

Accepted Answer

When the population standard deviation is unknown and the sample size is less than 30, we use the t distribution instead of the normal distribution. Therefore, the correct test statistic to use in this scenario is the t-statistic.

Question 13

As the Type II error β of a statistical test increases,the power of the test _____________.
A)Increases
B)Decreases
C)Stays the same
D)Randomly fluctuates

Accepted Answer

Power is the probability of correctly rejecting a false null hypothesis. As the Type II error increases, it means that the probability of failing to reject a false null hypothesis also increases. This implies that the power of the test decreases, as there is a higher chance of not detecting a significant difference when one exists. Therefore, the correct answer is B.

Question 14

To compute a 95 percent confidence interval for σ²,we use n - 1 degrees of freedom and the chi-square points on the distribution curve of χ_α/2² and of χ_1-(α/2)².

Accepted Answer

This is true. When computing a confidence interval for the population standard deviation, we use the chi-square distribution and (n-1) degrees of freedom. The critical values for the lower and upper bounds of the confidence interval are found using the chi-square points on the distribution curve of χ^2α/2 and χ^21-(α/2) with (n-1) degrees of freedom.

Question 15

____________ is the probability of not rejecting H₀ when H₀ is false. A)Type I error B)Type II error C)Random error D)α

Accepted Answer

The probability of not rejecting a false null hypothesis is known as the Type II error. Therefore, the correct answer is option B. Option A (Type I error) refers to rejecting a true null hypothesis. Option C (Random error) is a general term referring to any error that is unpredictable or lacks a specific cause. Option D (α) refers to the significance level, which determines the probability of making a Type I error.

Question 16

A(n)_____________ hypothesis is the statement that is being tested.It usually represents the status quo,and it is not rejected unless there is convincing sample evidence that it is false.
A)Research
B)Alternative
C)Null
D)True

Accepted Answer

A null hypothesis is a statement that assumes there is no association between variables or no difference between groups. It is usually the default position, and it is not rejected unless there is sufficient evidence to prove otherwise.

Question 17

Using a χ² test statistic to test the null hypothesis that the variance of a new process is equal to the variance of the current process and rejecting at a p-value less than α,we can conclude that the new process is more consistent than the current process.

Accepted Answer

The chi-square test statistic is used to test the null hypothesis that the variance of two populations are equal. If the p-value is less than alpha, we reject the null hypothesis and conclude that the variances are not equal. In this case, we can conclude that the new process is more consistent than the current process because a smaller variance indicates a more consistent process.

Question 18

When testing a hypothesis about a single mean,if the sample size is 51,and the population standard deviation is known,the correct test statistic to use is ___________.
A)r
B)z
C)t
D)p-value

Accepted Answer

When testing a hypothesis about a single mean with a known population standard deviation and a sample size greater than 30, we use a z-test. Therefore, the correct test statistic to use is z.

Question 19

Assuming that the null hypothesis is true,the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.
A)α
B)β
C)p-value
D)Type I error

Accepted Answer

The p-value is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data. It helps determine whether to reject or fail to reject the null hypothesis.

Question 20

When testing a hypothesis about a single mean,a sample size of 200 is selected from a normally distributed population.If the population standard deviation is known,the correct test statistic to use is ___________.
A)r
B)z
C)t
D)p-value

Accepted Answer

Since the population standard deviation is known, we can use the z-test for a single mean. The z-test assumes that the sample mean is normally distributed, which is approximately true when the sample size is large (n ≥ 30). In this case, the sample size is 200, so the z-test is appropriate.

Quiz 9: Hypothesis Testing

In order to make statistical inferences about σ² that are valid using a chi-square distribution,the assumption is that the sampled population is also a chi-square distribution.

A null hypothesis is not rejected at a given level of significance.As the assumed value of the mean gets further away from the true population mean,the type II error will _____________.

The ____________ hypothesis will be accepted only if there is convincing sample evidence that it is true.

χ²_α is the point on the vertical axis under the curve of the chi-square distribution that gives a right-hand tail area equal to α.

For a fixed sample size,the lower we set α,the higher is the ___________.

The rejection of a true null hypothesis is called a ______________ error.

When evaluating a new process,using the square root of the upper end of the confidence interval for σ² gives an estimate of the smallest that σ for the new process might reasonably be.

The ____________ hypothesis is not rejected unless there is sufficient sample evidence to do so.

The value of the test statistic is compared with a(n) _______________ in order to decide whether the null hypothesis can be rejected.

Assuming a fixed sample size,as α (Type I error) decreases,β (Type II error) ___________.

When testing a hypothesis about a single mean,if the sample size is 20,the population standard deviation is unknown,and the population is assumed to be a normal distribution,the correct test statistic to use is ___________.

As the Type II error β of a statistical test increases,the power of the test _____________.

To compute a 95 percent confidence interval for σ²,we use n - 1 degrees of freedom and the chi-square points on the distribution curve of χ_α/2² and of χ_1-(α/2)².

____________ is the probability of not rejecting H₀ when H₀ is false.

A(n) _____________ hypothesis is the statement that is being tested.It usually represents the status quo,and it is not rejected unless there is convincing sample evidence that it is false.

Using a χ² test statistic to test the null hypothesis that the variance of a new process is equal to the variance of the current process and rejecting at a p-value less than α,we can conclude that the new process is more consistent than the current process.

When testing a hypothesis about a single mean,if the sample size is 51,and the population standard deviation is known,the correct test statistic to use is ___________.

Assuming that the null hypothesis is true,the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.

When testing a hypothesis about a single mean,a sample size of 200 is selected from a normally distributed population.If the population standard deviation is known,the correct test statistic to use is ___________.

Quiz 9: Hypothesis Testing

In order to make statistical inferences about σ2 that are valid using a chi-square distribution,the assumption is that the sampled population is also a chi-square distribution.

A null hypothesis is not rejected at a given level of significance.As the assumed value of the mean gets further away from the true population mean,the type II error will _____________.

The ____________ hypothesis will be accepted only if there is convincing sample evidence that it is true.

χ2α is the point on the vertical axis under the curve of the chi-square distribution that gives a right-hand tail area equal to α.

For a fixed sample size,the lower we set α,the higher is the ___________.

The rejection of a true null hypothesis is called a ______________ error.

When evaluating a new process,using the square root of the upper end of the confidence interval for σ2 gives an estimate of the smallest that σ for the new process might reasonably be.

The ____________ hypothesis is not rejected unless there is sufficient sample evidence to do so.

The value of the test statistic is compared with a(n) _______________ in order to decide whether the null hypothesis can be rejected.

Assuming a fixed sample size,as α (Type I error) decreases,β (Type II error) ___________.

When testing a hypothesis about a single mean,if the sample size is 20,the population standard deviation is unknown,and the population is assumed to be a normal distribution,the correct test statistic to use is ___________.

As the Type II error β of a statistical test increases,the power of the test _____________.

To compute a 95 percent confidence interval for σ2,we use n - 1 degrees of freedom and the chi-square points on the distribution curve of χα/22 and of χ1-(α/2)2.

____________ is the probability of not rejecting H0 when H0 is false.

A(n) _____________ hypothesis is the statement that is being tested.It usually represents the status quo,and it is not rejected unless there is convincing sample evidence that it is false.

Using a χ2 test statistic to test the null hypothesis that the variance of a new process is equal to the variance of the current process and rejecting at a p-value less than α,we can conclude that the new process is more consistent than the current process.

When testing a hypothesis about a single mean,if the sample size is 51,and the population standard deviation is known,the correct test statistic to use is ___________.

Assuming that the null hypothesis is true,the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.

When testing a hypothesis about a single mean,a sample size of 200 is selected from a normally distributed population.If the population standard deviation is known,the correct test statistic to use is ___________.

In order to make statistical inferences about σ² that are valid using a chi-square distribution,the assumption is that the sampled population is also a chi-square distribution.

χ²_α is the point on the vertical axis under the curve of the chi-square distribution that gives a right-hand tail area equal to α.

When evaluating a new process,using the square root of the upper end of the confidence interval for σ² gives an estimate of the smallest that σ for the new process might reasonably be.

To compute a 95 percent confidence interval for σ²,we use n - 1 degrees of freedom and the chi-square points on the distribution curve of χ_α/2² and of χ_1-(α/2)².

____________ is the probability of not rejecting H₀ when H₀ is false.

Using a χ² test statistic to test the null hypothesis that the variance of a new process is equal to the variance of the current process and rejecting at a p-value less than α,we can conclude that the new process is more consistent than the current process.