Question 1

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

Accepted Answer

As you set alpha lower and lower, you increase your chances of committing a Type II error and thus decreasing your power of finding the correct statistical conclusion.

Question 2

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 ________.

Accepted Answer

Since you do not know the population standard deviation, you can to use the t test.

Question 3

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 4

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 5

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

Accepted Answer

We have to compare the test statistic (something we calculate from the data) to the critical value (something we set before we begin the statistical tests).

Question 6

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 ________.

Accepted Answer

Since you know the population standard deviation, you can perform the z test.

Question 7

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

Accepted Answer

This statement is assigned the burden of proof. This is what we are trying to prove, but can only do so with enough statistical evidence.

Question 8

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 1,500 voting age citizens. 1,020 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.

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 9

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 ________.

Accepted Answer

A Type II error is failing to reject a null hypothesis that is not true, and if the assumed value of the mean is far from the true mean, then you should reject the null.

Question 10

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 when applying the p-value rule, we are rejecting at a p-value less than α, we can conclude that the new process is more consistent than the current process.

Accepted Answer

This is true because if the p-value was greater than alpha, the two processes would have had the same consistency.

Question 11

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

Accepted Answer

They are inversely related.

Question 12

Rejecting a true null hypothesis is called a ________ error.

Accepted Answer

This means that you actually did not have enough statistical evidence to reject the null hypothesis.

Question 13

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.

Accepted Answer

The null is the status quo, something that is not disputed-it is the complement to the alternative hypothesis.

Question 14

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 15

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

Accepted Answer

This is because we are giving ourselves very little room for error and thus increase our chances of failing to reject the null when it should be rejected.

Question 16

________ is not rejecting H₀ when H₀ is false.

Accepted Answer

This means that you had enough statistical evidence to reject the null hypothesis, but you did not.

Question 17

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 χ²_α_/2 and of χ²₁₋₍_α_/2).

Accepted Answer

In this situation, we once again reject the null if the p-value is less than alpha. One area (either to the right or the left) will be smaller.

Question 18

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

Accepted Answer

The null hypothesis is given the benefit of the doubt and is not rejected unless there is convincing sample evidence that it is false.

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.

Accepted Answer

In the p-value rule approach, we collect sample data and compute the value of the test statistic. We then compute the p-value, which measures the likelihood of observing the computer test statistic value if the null hypothesis is true.

Question 20

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 ________.

Accepted Answer

Since the standard deviation is known, you can complete the z test.

Quiz 10: Hypothesis Testing