Deck 8: Hypothesis Testing Using the One-Sample T-Test

Question 1

What happens to the absolute value of $t_{\mathrm{crit}}$ as df increases? It

A)decreases.
B)increases.
C)remains the same.
D)increases or decreases depending on whether $t_{o b t}$ is positive or negative.

Answer 1

decreases.

Question 2

Suppose we have a 95% confidence interval of 12.23 and 16.75.What does this mean?

A)We are 95% confident that the true population mean is between 12.23 and 16.75.
B)We are 95% confident that the true population mean is either 12.23 or 16.75.
C)The average of 12.23 and 16.75 is probably the true population mean.
D)We are at least 95% certain that neither a Type I nor a Type II error was made.

Answer 2

A

Question 3

Which of the following requirements is common to both the z-test and the one-sample t-test?

A)Alpha is selected to be 0.01.
B)The raw score population forms a normal distribution, and the population mean and standard deviation are known.
C)The standard deviation of the raw score population is estimated by $S_{X}$ .
D)There is one random sample of interval or ratio scores.

Answer 3

There is one random sample of interval or ratio scores.

Question 4

For a two-tailed test with α = 0.05, the $t_{\mathrm{crit}}$ value is

A)either +1.96 or -1.96.
B)both +1.96 and -1.96.
C)either +1.645 or -1.645.
D)different for each df.

Question 5

Which of the following is one of the requirements of a one-sample t-test?

A)The obtained scores are either ordinal or interval.
B)The population standard deviation is estimated by computing $S_{X}$ .
C)The population standard deviation is known.
D)The population distribution is skewed.

Question 6

Which of the following would make it more likely your t-test will be significant?

A)Decreasing the degrees of freedom
B)Using a one-tailed test rather than a two-tailed test
C)Changing α from 0.05 to 0.01
D)Computing a confidence interval for μ

Question 7

What does the $t_{o b t}$ value indicate?

A)The probability of rejecting the null hypothesis
B)The probability of retaining the null hypothesis
C)How far the population mean, μ, is from the mean of the sampling distribution of means
D)How far the sample mean is from the μ of the sampling distribution of means

Question 8

Unless we use the correct from the t-distribution for the appropriate N, $\begin{array}{c}t_{\text {crit }} \\H_{0} \\H_{0}\end{array}$

A)we will fail to reject .
B)we will always reject .
C)the probability of making a Type I error will increase.
D)the probability of making a Type I error will not equal α.

Question 9

When is a sample mean likely to represent a particular population mean?

A)It depends on sampling error.
B)It depends on our alpha.
C)When our t-obtained is greater than the expected value of t.
D)When we reject the null hypothesis.

Question 10

Interval estimation suggests a where we expect the to fall.

A)range of values; population parameter
B)specific value; population parameter
C)range of values; sample mean
D)specific value; sample mean

Question 11

Suppose a poll has been conducted on Americans' favorable attitudes towards a certain issue.If it is reported that Americans are 56%+4% in favor of the issue, which of the following is not a possible value represented within the margin of error?

A)51%
B)53%
C)56%
D)60%

Question 12

When is a t-test used instead of a z-test?

A)When the population μ is known
B)When the population deals with two samples
C)When the population standard deviation is known
D)When the population standard deviation is unknown

Question 13

For a given level of α, when does $t_{c r i t}=Z_{c r i t}$ ?

A)When the degrees of freedom for the t-test equal the degrees of freedom for the z-test
B)When the degrees of freedom for the t-test equal N for the z-test
C)When the degrees of freedom for the t-test are greater than 120
D)There is never a situation when $t_{c r i t}=Z_{c r i t}$

Question 14

To achieve statistical significance for a one-sample t-test,

A)the t-obtained must be larger than the t-critical.
B)the t-obtained must equal the t-critical.
C)the t-obtained must be less than the t-critical.
D)the t-obtained must differ from the t-critical by .05.

Question 15

How is the t-distribution defined?

A)The distribution of all possible values of t
B)How far the sample mean is from the μ of the sampling distribution in estimated standard error units
C)The distribution of all possible values of t for random samples having the same N from the population described by $H_{0}$
D)The distribution of all possible values of t for random samples having the same N from the population described by $H_{a}$

Question 16

The precise location on the dependent measure where we expect our population mean to fall refers to

A)point estimation.
B)interval estimation.
C)margin of error.
D)confidence interval.

Question 17

After determining your one-tailed t-test is significant, what should you do?

A)See if the test is still significant at a lower α.
B)See if the test is still significant at a higher α.
C)See if the test is still significant if you use a two-tailed test.
D)Compute a confidence interval for μ.

Question 18

Which of the following is not one of the steps in a one-sample t-test?

A)Create the null hypothesis H₀) and alternative hypothesis H_a).
B)Create the sampling t-distribution and find in the t-tables.
C)Compute .
D)Compare to .

Question 19

Colin has computed the variance for his 10 raw scores and obtained = 16.37.He then computed $S_{X}^{2}$ $S \bar{X}$ as follows: $s \bar{x}=\sqrt{\frac{4.046}{10}}=0.636$ What is wrong?

A)Colin first took the square root of $S_{X}^{2}$ and put this into the formula for $S \bar{X}$ .He should have used the $S_{X}^{2}$ = 16.37 value.
B)Colin should have divided here by N - 1.
C)Colin should not have taken the square root of 4.046/10 because he needs $S_{X}^{2}$ in the formula for the t-test.
D)There is nothing wrong with the way Colin has done this problem.

Question 20

What is $S \bar{X}$ ?

A)The estimated population standard deviation
B)The population standard deviation
C)The estimated standard error of the mean
D)The standard error of the mean

Question 21

Using the following data, calculate the standard error of the mean.
55 48 59 50 48 52 50 48 57 54
50 52 54 43 44 53 40 46 50 51

Question 22

Using the data given below, perform a two-tailed t-test to compare the sample mean to μ = 35.5.Use α = .05

Question 23

Using the following data, conduct a two-tailed t-test.Use a known population mean of 49 and α = .01.
51 48 52 50 48 52 50 48 52 54
50 52 54 47 49 53 47 46 50 51

Question 24

Using the following data, conduct a one-tailed t-test in the upper tail.Use a known population mean of 49 and α =
.05.
51 48 52 50 48 52 50 48 52 54
50 52 54 47 49 53 47 46 50 51

Question 25

Using the following data, conduct a two-tailed t-test.Use a known population mean of 49 and α = .05.
51 48 52 50 48 52 50 48 52 54
50 52 54 47 49 53 47 46 50 51

Question 26

If a researcher reports a one-sample t-test with df = 24, how many individuals participated in this study?

Question 27

Using the following data, compute the t-statistic.Use a known population mean of 28, a two-tailed test, and = 0.05.
22 19 23 26 18 22 21
31 30 25 20 24 25 23

Question 28

Conduct a two-tailed t-test for and μ = 48.Use α = .05.Calculate the .

Question 29

Conduct a two-tailed t-test for and μ = 87.Use α = .05.What is the value of ?

Question 30

Using the following data, compute the t-statistic.Use a known population mean of 20, a one-tailed test in the upper tail, and = 0.05..
22 19 23 26 18 22 21
31 30 25 20 24 25 23

Question 31

For and what is ?

Question 32

Using the following data, calculate the sample standard deviation.
55 48 59 50 48 52 50 48 57 54
50 52 54 43 44 53 40 46 50 51

Question 33

Suppose you conduct an experiment with 20 subjects and the turns out to be 0.69, which is not statistically significant.What is the correct way to report your results?

Question 34

Using the following data, conduct a one-tailed t-test in the upper tail.Use a known population mean of 49 and α =
.05.
55 48 59 50 48 52 50 48 57 54
50 52 54 43 44 53 40 46 50 51

Question 35

Using the following data, calculate the sample mean.
55 48 59 50 48 52 50 48 57 54
50 52 54 43 44 53 40 46 50 51

Question 36

Suppose we have a sample mean of 12, estimate standard error of the mean of 2.5, and a t-critical value of 2.306.What would be the lower and upper limits of our confidence interval?

Question 37

Some people claim psychology is common sense.If this is true, then students who have not taken psychology courses should be able to predict the outcomes of experiments as well as psychology majors.If it is not, nonpsychology students should perform worse than psychology students.Psychology students typically predict outcomes with μ = 69% accuracy.A sample of 15 nonpsychology students predicted with = 60% accuracy.The = 2.606.If appropriate, calculate the 95% confidence interval for nonpsychology students.

Question 38

Suppose you conduct a one-tailed t-test and your results are significant at both the .05 and .01 levels.What should you report and why?

Question 39

What are the two basic consequences of going from a 95% to a 99% confidence interval?

Question 40

Using the following data, conduct a two-tailed t-test.Use a known population mean of 49 and α = .05.
55 48 59 50 48 52 50 48 57 54
50 52 54 43 44 53 40 46 50 51

Question 41

Identify the major difference between the z- and t-obtained formulas.

Question 42

Suppose you've read about a poll conducted by a certain media outlet surveying the popularity of the U.S.President.This poll puts the President's approval rating at 49.7% +3.5%.Would would be the range that we would expect the actual population values to fall?

Question 43

What is the name of the procedure we can use in the unlikely event that our t-obtained value falls between two t- critical values in the t-table?

Question 44

Suppose you're computing a one-sample t-test and you just finished computing your t-obtained.What is the next step for you to take?