Deck 9: One-Sample T-Test

Question 1

When using the t-statistic,

A) the value of σ is known.
B) the value of σ is unknown.
C) we can directly calculate a value for σ.
D) a standard deviation is not needed.

Answer 1

B

Question 2

The denominator in the formula for the t-statistic is __________.

A) s_M
B) σ_M
C) σ
D)

Answer 2

A

Question 3

The t-distribution is used if

A) samples are larger than 60.
B) the population mean is not known.
C) the population standard deviation is known.
D) the population standard deviation is unknown.

Answer 3

D

Question 4

If the population standard deviation is not known, which statistical test should be used?

A) the z test
B) the t test
C) the standard deviation test
D) the variance test

Question 5

Which of the following is NOT needed in order to use the one-sample t test?

A) μ
B) M
C) σ_M
D) s_M

Question 6

The t-distribution is a ______________ distribution whose shape changes according to the ________________.

A) theoretical; size of the sample
B) empirical; size of the sample
C) theoretical; standard deviation
D) empirical; standard deviation

Question 7

The t-distribution is a family of curves. The particular t-distribution that is used for a hypothesis test will be based on ________________.

A) σ
B) σ_M
C) df
D) s_M

Question 8

Given a sample size of 48, the df for a one-sample t test would be _________.

A) 46
B) 47
C) 48
D) 49

Question 9

If df is 20 for a one-sample t test, what is the sample size?

A) 19
B) 18
C) 22
D) 21

Question 10

In comparison to the normal distribution, as df increase, the t-distribution

A) becomes flatter.
B) has t-values that extend further into the tails.
C) becomes increasingly similar in shape to the normal distribution.
D) is wider that the normal distribution.

Question 11

Which of the following statements is true regarding the t-distribution?

A) Larger samples make it easier to reject H₀.
B) Smaller samples make it easier to reject H₀.
C) Sample size does not affect the ability to reject H₀.
D) The t-distribution is based on an infinite number of cases.

Question 12

Which of the following is false regarding the table for the t-distribution?

A) Sample size (n) is listed in the left column.
B) The alpha level will need to be halved for two-tailed tests.
C) If the particular df for your sample size is not shown, you should use the next highest df.
D) All of the above statements are false.

Question 13

An obtained t-value that falls close to the population mean

A) has a high probability of occurrence.
B) has a low probability of occurrence.
C) will likely reject the H₀.
D) both "b" and "c" are true.

Question 14

Given a t_crit = ±2.94, which of the following obtained t-values will reject the H₀?

A) +1.58
B) -2.58
C) -3.58
D) +2.72

Question 15

Given a t_crit = -2.08, which of the following obtained t-values will reject H₀?

A) +2.62
B) -2.10
C) -1.98
D) +2.06

Question 16

The number in parentheses ( ) just before the reported t-value in the results section (step four) of a hypothesis test is

A) n
B) df
C) α
D) t_crit

Question 17

If the results of a t test include the statement that "p > .01," then

A) you will fail to reject H₀.
B) you will reject H₀.
C) your obtained t-value has a low probability of occurrence.
D) you have gained support for H₁.

Question 18

If the results of a t test include the statement that "p < .05," then

A) you will fail to reject H₀.
B) your obtained t-value has a high probability of occurrence.
C) you have gained support for H₁.
D) the result is not significant.

Question 19

An obtained probability for a t test that is greater than alpha

A) will lead to rejection of H₀.
B) is statistically significant.
C) is unlikely if H₀ is true.
D) will fail to reject H₀.

Question 20

An obtained probability for a t test that is less than alpha

A) will fail to reject H₀.
B) is not statistically significant.
C) is unlikely if H₀ is true.
D) is likely due to chance.

Question 21

Which is the correct notation for the standard error of the mean for a one-sample t test?

A) σ
B) σ_M
C) s
D) s_M

Question 22

A population has a known mean of 50. A researcher believes that a particular treatment will increase scores and conducts a one-sample t test. What is the null hypothesis?

A) H₀: μ = 50
B) H₀: μ ≠ 50
C) H₀: μ ≥ 50
D) H₀: μ ≤ 50

Question 23

The population mean for scores on an anxiety scale is 28. A researcher obtains a representative sample and implements a treatment designed to decrease anxiety scores. A one-sample t test is conducted. What is the null hypothesis?

A) H₀: μ = 28
B) H₀: μ ≠ 28
C) H₀: μ ≤ 28
D) H₀: μ ≥ 28

Question 24

A population has a known mean of 62. A researcher implements a new treatment to a sample to determine if it has an effect on the dependent variable. What is the null hypothesis?

A) H₀: μ = 62
B) H₀: μ ≠ 62
C) H₀: μ ≥ 62
D) H₀: μ ≤ 62

Question 25

A researcher is conducting a one-sample t test to see if a particular intervention has any effect on the dependent variable. Alpha is .05 and n = 18. What is t_crit?

A) +1.740
B) +1.734
C) ±2.101
D) ±2.110

Question 26

A researcher is conducting a one-sample t test to determine if a particular treatment intervention will lower scores on a dependent variable. α = .01 and n = 43. What is t_crit?

A) -2.423
B) ±2.423
C) +2.423
D) -2.704

Question 27

A population has a known mean of 65. A one-sample t test is conducted to determine if a treatment will influence scores on the dependent variable. What is the alternative hypothesis?

A) H₁: μ = 65
B) H₁: μ ≠ 65
C) H₁: μ > 65
D) H₀: μ = 65

Question 28

The population mean on a standardized math test is 75. A tutoring program is implemented at a local college to determine if the math scores would improve as a result. A one-sample t test is conducted. What is the alternative hypothesis?

A) H₁: μ ≥ 75
B) H₁: μ ≠ 75
C) H₁: μ > 75
D) H₀: μ = 75

Question 29

A new medication shows promising results in reducing the intensity of symptoms in people who suffer from depression. The population mean on a depression inventory is 25. A one-sample t test is administered to a sample of subjects taking the medication. What is the alternative hypothesis?

A) H₁: μ = 25
B) H₁: μ ≠ 25
C) H₁: μ < 25
D) H₀: μ ≤ 25

Question 30

A population mean is 45. A one-sample t test is conducted with n = 9 subjects and results in a sample mean of 48 with a s = 5. What is t_obt?

A) +1.80
B) -1.80
C) +5.36
D) -5.36

Question 31

A population mean is μ = 85. A one-sample t test is conducted with n = 25 subjects. The test resulted with a sample mean of M = 81 and s_M = 1.46. What is t_obt?

A) +1.87
B) -1.87
C) +2.74
D) -2.74

Question 32

A one-sample t test is conducted which resulted in a significant effect. The sample mean was 42 based on a sample size of n = 16. The population mean was 50 with s = 2.33. What was Cohen's d effect size?

A) 3.43
B) .86
C) .13
D) 2

Question 33

A one-sample t test was conducted which resulted in a significant effect. The sample mean was 95 based on a sample size of n = 25. The population mean was 90 with an estimated standard deviation of 8.42. What was Cohen's d effect size?

A) 2.98
B) -2.98
C) +.59
D) -.59

Question 34

Given M = 26, n = 9, μ = 23, and s = 6.2, Cohens's d is _______, which is considered to be a ______________ effect.

A) .48; small
B) .48; moderate
C) 1.44; large
D) 1.44; extra large

Question 35

Which of the following is not one of the assumptions for a one-sample t test?

A) Independent and random selection of subjects.
B) The dependent variable is normally distributed in the population.
C) The dependent variable can be measured on an interval or ratio scale.
D) σ is known.

Question 36

When would you use a one-sample t test rather than a z-test?

Question 37

How does sample size (and therefore df) affect the ability to reject the null hypothesis of a t test?

Question 38

What are the two main uses of the one-sample t test?

Question 39

Determine t_crit for the following situations and decide if H₀ should be rejected. For the one-tailed tests, assume that the researcher is looking for score increases.

Question 40

Describe two potential problems which would make the following conclusion problematic: "The medication had no significant effect. Reject H₀, t(32) = +1.92, p > .05."

Question 41

Given s = 8 and n = 32, calculate the standard error of the mean.

Question 42

For a one-sample t test, H₀: μ = 20. Given M = 18, s = 3, and n = 12, what is t_obt?

Question 43

A population has a known mean of 98 with s = 18. Can H₀ be rejected at a .05 level of significance, two-tailed, if M = 104 with a sample size of 64?

Question 44

A student success coach enlisted the assistance of the college's statistician to determine if her new study skills program will have any effect on entrance exam scores. The mean on the exam for new students who do not go through the program is μ = 76. The program is implemented over the summer before classes start in the fall. A sample of these students are tested and obtain a M = 79.
a. Write the null and alternative hypotheses in words.
b. Write the null and alternative hypotheses in symbolic notation.

Question 45

Fear of public speaking is reported to be one of the greatest fears that people have. The population mean on a public speaking anxiety scale is μ = 50. A performing arts instructor believes that students who major in the theater have less anxiety about public speaking than the general population. She decides to test her hypothesis by administering the public speaking anxiety test to a sample of theater majors. A sample mean of M = 48 is obtained.
a. Write the null and alternative hypotheses in words.
b. Write the null and alternative hypotheses in symbolic notation.

Question 46

A researcher wants to conduct a one-sample t test on a population that has a μ = 35. He believes that he has an intervention which will increase scores. State the null and alternative hypotheses in symbolic notation.

Question 47

Write tcrit for each of the following situations:
a. n = 22; α = .05, two-tailed
b. n = 36; α = .01, two-tailed
c. n = 16; α = .05, one-tailed (the researcher believes treatment will increase scores)
d. n = 9; α = .10, one-tailed (the researcher believes treatment will decrease scores)

Question 48

A normally distributed population has a μ = 100. After a treatment procedure is implemented to a sample of size n = 36, a sample mean of M = 91 is obtained with a s = 20. Did treatment significantly lower scores? Test at α = .01.

Question 49

The national average on the ACT math test is 20.5. A sample of n = 9 incoming college freshmen is tested at a local university. The mean of the sample is M = 22.7 with a s = 4. Does the sample mean differ significantly from the national average? Test at α = .05.

Question 50

A particular make and model of an automobile is advertised to get 36 miles per gallon (MPG) of gasoline. A representative from a "Truth in Advertising" organization samples 5 vehicles of that make and model which earned the following MGP scores: 38, 40, 35, 37, and 41. Conduct a one-sample t test to determine if the MPG of the sample models differs significantly from that which was advertised. Use α = .05.