True or False: Mathematically, the normal distribution and the t-distribution are very differ-
ent. - ANSWER False
Unlike the normal distribution, the t-distribution is sensitive to _________.
Sample size
Error
Time
Bias - ANSWER Sample size
A ______ -test is used if the population standard deviation is known, whereas a ______ -test
is used if the population standard deviation is estimated from the sample standard devia-
tion.
t; z
z; r
z; t
r; t - ANSWER z; t
What is the meaning of the null hypothesis (Ho) for a one sample t-test? - ANSWER The
population mean (𝜇) is equal to the hypothetical population mean (𝜇o).
If a researcher states in the alternative hypothesis that μ is greater than the claimed value,
what type of test would be performed? - ANSWER right-tailed test
Define degrees of freedom.
1
, What is the formula for calculating the degrees of freedom for a one sample t test? An inde-
pendent samples t-test? A paired samples t-test? - ANSWER The number of values that
may vary freely until remaining values are determined.
df for one-sample and paired samples: df = n-1
df for independent samples: df total = df1 + df2 = n1 + n2 - 2
Admissions counselors at a local college claim that the IQ scores of their students are greater
than the average IQ. They select 11 college students and measure their IQ scores.
111 98 118 100 94 110 123 110 99 96 120
The sample statistics calculated are as follows: n = 11, x-bar = 107.1818, and s = 10.3133.
Conduct a one sample t-test (a=0.05) to test the claim that this sample of students has a
mean IQ score greater than 100 (which is the mean IQ score of the general population). Re-
port the results in APA format. - ANSWER t(10)= 2.31, p<0.05, one tailed.
Calculate the effect size (d) of the sample xbar =109.5, 𝜇 =100, and s =5.2. Interpret the re-
sult. - ANSWER 1.83 Large effect
Construct an 80% confidence interval for a two-tailed t test with x-bar = 46, 𝜇= 50, s= 4.7434,
n= 10. - ANSWER CI [43.93, 48.07]
Given the sample statistics: n =11, xbar =107.1818, and s =10.3133. Compare the critical t
value for a one-tailed test and a two-tailed test with α=0.05. Why is there a difference? - AN-
SWER In a two-tailed test, the 0.05 is split between the two tails rather than being con-
centrated on either the left or right side of the distribution. Therefore, the corresponding
critical value would change. Specifically, the critical value for a two-tailed test (α=0.05)
would be ±2.228 and the critical t value for a one-tailed test is ±1.812.
In what type of experimental design is an assessment administered before and after a treat-
ment condition with the same participants?
2
ent. - ANSWER False
Unlike the normal distribution, the t-distribution is sensitive to _________.
Sample size
Error
Time
Bias - ANSWER Sample size
A ______ -test is used if the population standard deviation is known, whereas a ______ -test
is used if the population standard deviation is estimated from the sample standard devia-
tion.
t; z
z; r
z; t
r; t - ANSWER z; t
What is the meaning of the null hypothesis (Ho) for a one sample t-test? - ANSWER The
population mean (𝜇) is equal to the hypothetical population mean (𝜇o).
If a researcher states in the alternative hypothesis that μ is greater than the claimed value,
what type of test would be performed? - ANSWER right-tailed test
Define degrees of freedom.
1
, What is the formula for calculating the degrees of freedom for a one sample t test? An inde-
pendent samples t-test? A paired samples t-test? - ANSWER The number of values that
may vary freely until remaining values are determined.
df for one-sample and paired samples: df = n-1
df for independent samples: df total = df1 + df2 = n1 + n2 - 2
Admissions counselors at a local college claim that the IQ scores of their students are greater
than the average IQ. They select 11 college students and measure their IQ scores.
111 98 118 100 94 110 123 110 99 96 120
The sample statistics calculated are as follows: n = 11, x-bar = 107.1818, and s = 10.3133.
Conduct a one sample t-test (a=0.05) to test the claim that this sample of students has a
mean IQ score greater than 100 (which is the mean IQ score of the general population). Re-
port the results in APA format. - ANSWER t(10)= 2.31, p<0.05, one tailed.
Calculate the effect size (d) of the sample xbar =109.5, 𝜇 =100, and s =5.2. Interpret the re-
sult. - ANSWER 1.83 Large effect
Construct an 80% confidence interval for a two-tailed t test with x-bar = 46, 𝜇= 50, s= 4.7434,
n= 10. - ANSWER CI [43.93, 48.07]
Given the sample statistics: n =11, xbar =107.1818, and s =10.3133. Compare the critical t
value for a one-tailed test and a two-tailed test with α=0.05. Why is there a difference? - AN-
SWER In a two-tailed test, the 0.05 is split between the two tails rather than being con-
centrated on either the left or right side of the distribution. Therefore, the corresponding
critical value would change. Specifically, the critical value for a two-tailed test (α=0.05)
would be ±2.228 and the critical t value for a one-tailed test is ±1.812.
In what type of experimental design is an assessment administered before and after a treat-
ment condition with the same participants?
2
