Practice Questions 6.1

Click the two reasons that the method of hypothesis testing is needed.

A. To find out if a hypothesis about the value of the population mean makes sense.
B. To find out how reasonable a chosen value is the population mean.
C. To find out if it is reasonable to write a hypothesis about the value of the population mean.
D. To find out if the population mean is less than, or greater than, a chosen value.

In hypothesis testing, what does reasonableness mean?

A.  How close a chosen value is to the population mean.
B. How reasonable the chosen value and the value of the population mean are different.
C. How likely a reasonable person would agree with a chosen value.
D. How reasonable is the hypothesis about the value of the population mean.

In hypothesis testing, what does less than, or greater than, mean?

A. The population mean could have a value.
B. The population mean could have a value of -∞ , and +∞.
C. The population mean could have a value of zero (0).
D.  The population mean could have a value of -∞ , or +∞.

Please match the following inequalities, and equality, to their meaning in a distribution.

A. Not equal to
B. Greater than
C. Less than

__ A one-tail to the left situation
__ A one-tail to the right situation
__ A two-tail situation.

Click the two assumptions needed for the method of hypothesis testing.

A. The individuals were randomly selected.
B. The sample size is greater than 30 data values.
C. The sample average is normally distributed.
D. The data values are normally distributed.

In hypothesis testing, where does the hypothesized value NOT come from?

A. From the researcher's educated opinion. 
B. From an expert in the field of study.
C. From the results of prior research.
D.  From the results of the sample.

In hypothesis testing, how is close and far determined?

A.  By converting the situation from the sample distribution into the z, or t, distribution.
B. By the mathematical distance between the sample average and the hypothesized mean.
C. By comparing the sample average to its z-score, or t-value.
D. By using a ruler on a schematic curve.

Where does the value of a test statistic come from?

A. From the result of a hypothesis test.
B. From the researchers point of interest.
C.  From converting the sample average into a z-score, or t-value.
D. From the z-table, or t-table.

Why is the method of hypothesis testing called an inferential method of statistics?

A.  Because it gives the best guess (infers) from the sample for the value of the population mean.
B. Because it infers whether the researcher's belief is correct, or not.
C. Because it infers the end result.
D. Because it uses similar mathematics to a confidence interval, which is an inferential method.

How does the method of hypothesis testing make an inference (i.e. draw a conclusion) about a population mean?

A. By seeing if the value of the test statistic is less than zero (0).
B. By seeing if the test statistic is inside the critical region.
C.  By seeing if the test statistic is closer to zero (0), or farther from zero, than the critical value.
D. By seeing if the critical value is inside the confidence interval.

Click all choices that are steps in the General Method to solve problems in statistics.

A. Step A: Abstract - Relevant information from the question.
B. Step 1: Theorize - Probability information from theory.
C. Step 2: Analyze - Sample information from the abstraction step.
D. Step 3: Infer - Population information from the analyze step.

Click all choices that are steps in Step A: Abstract of the General Method to solve problems in statistics.

A. Get descriptive statistics from the sample data values.
B. Find the critical value from probability.
C. Calculate the test statistic from the sample information.
D. Write a set of two hypotheses about the researcher's question.

Click which choice is NOT a descriptive statistic:

A.  x̄
B.  t0
C. n
D. S

What information does the null hypothesis express?

A. The preferred outcome of the hypothesis test.
B. A mathematical interval for the population mean.
C.  The currently believed value of the population mean.
D. The researcher's believed value of the population mean.

What information does the alternative hypothesis express?

A. The preferred outcome of the hypothesis test.
B.  The researcher's believed value of the population mean.
C. A mathematical interval for the population mean.
D. The currently believed value of the population mean.

The null hypothesis always contains an equal sign.

True
False
True False

Click all choices that are steps in Step 1: Theorize of the General Method to solve problems in statistics.

A. Use the critical value to find the appropriate probability.
B. Calculate the test statistic to be able to make a statistical inference.
C. Use the schematic curve to analyze the situation from a statistical point of view.
D. Find the appropriate critical value(s) for this situation.

Please match each situation below with the information that goes in the middle of the schematic curve.

A.  Do a hypothesis test
B.  Find a confidence interval
C.  Find probability

__ The known value of the population mean.
__ The value of the sample average.
__ The hypothesized value of the population mean.

Please match each region below with the appropriate area under a schematic normal curve.

A.  The acceptance region
B.  The rejection region.

__ The body area of the schematic normal curve.
__ One, or both, tail area(s) of the schematic normal curve.

Click which choice below is NOT an appropriate rejection region.

A.  A middle body area.
B. A right tail area.
C. A two tail area.
D. A left tail area.

Please match each alternative hypothesis below with the appropriate statistical situation.

A.  H1: μ<0
B. H1: μ≠0
C. H1: μ>0

__ A two-tail situation means the critical value is positive and negative.
__ A right-tail situation means the critical value is positive.
__ A left-tail situation means the critical value is negative.

Click all choices that are steps in Step 2: Analyze of the General Method to solve problems in statistics.


A. Find the p-value from the test statistic.
B. Find the critical value from probability information.
C. Calculate the test statistic from sample information.
D. Use the test statistic and the critical value to make a statistical inference.

Where does the value of the test statistic come from?

A. From the t-equation

B. From the t-table
(t0= 2.359)
C. From the confidence interval
(CI%= x̄ + t(s / √n)
D. From a previously known value of the population mean

Click all choices that are the definition of p-value. (1)

A.  The area in one (or two) tail(s) from the value of the test statistic.
B. The area in one (or two) tail(s) from the value of the critical value.
C. The t-value of the test statistic.
D. The area between the test statistic and the critical value.

Click the two conclusions possible in Step 3: Infer of the General Method to solve problems in statistics.

A. Do NOT REJECT the null hypothesis.
B. Do REJECT the alternative hypothesis.
C. Do NOT REJECT the alternative hypothesis.
D. Do REJECT the null hypothesis.

What does Reject the Null Hypothesis mean?

A. That the null hypothesis is closer to the truth.
B.  That the alternative hypothesis is closer to the truth.
C. That the researcher prefers the alternative hypothesis.
D. That the null hypothesis is improperly written.

In a hypothesis test, click the possible approaches that can be used to make a conclusion in Step 3: Infer.

A. The Critical Value approach.
B. The p-Value approach.
C. The Test Statistic approach.
D. The Confidence Interval approach.

The Confidence Interval approach can only be used in a two-tail situation.

True
False
True False

In a hypothesis test, what is the size of the Type I error?

A.  Alpha (α).
B. Gamma (χ).
C. Beta (β).
D. Delta (δ).

A statistically significant result always means a practically significant result to be followed in practice.

True
False
True False