Chapter 9 Introduction to the t Statistic
In what circumstances is the t statistic used instead of a z-score for a hypothesis test?
C.The t statistic is used when the population variance (or standard deviation) is unknown
T OR F: A researcher reports a t statistic with df =30. This statistic was computed for a sample of n=29 scores.
False. A sample of n=31 would have a df=30
T or F: As the value of df increases, the t distribution tends to become flatter and more spread out.
False. As df increases the t distribution becomes taller and more compact like normal shaped distribution
T OR F:A sample of n=25 scores with a sample variance of s2 =100 would have an estimated standard error of 4 points.
False. The estimated SE is 4
T or F: In a hypothesis test, the larger the value for the sample variance, the more likely it is that you will reject the null hypothesis.
False. The larger the sample variance the less likely it is you reject the null hypothesis.
T or F: For a two-tailed hypothesis test with a=.05 and a sample of n=25 scores, the boundaries for the critical region would be t=+2.060
False. df=24 +2.064
T OR F: To calculate a t statistic, you must first compute the sample mean and the sample variance (or sample deviation)
TRUE
T or F: In a T statistic the estimated standard error provides a measure of how much difference is reasonable to expect between a sample mean and the population mean
True
T or F: In a hypothesis test, a t statistic near zero indicates that the sample mean is relatively close to the population mean that is specified in the null hypothesis.
True
T or F: Measure the effect size (such as Cohen's d and r2) are relatively unaffected by the size of the sample.
True
Which of the following is a difference between a hypothesis test with the t statistic and a test with a z-score?
a. You must use a different table to find critical values for the t test than for the test than for the z-score test. c. you must know the populataion variance (or standard deviation) for the z-score but not for the t statistic. d. you must calculate the sample variance (or standard deviation) for the t statistic but not for the z-score.
What is the estimated standard error for a sample of n=0 scores with s2=36
a. the square root of (36/9)
As sample variance increases, what happens to the likelihood of rejecting the null hypothesis and what happens to measures of effect size such as r2 and Cohen's d?
b. The likelihood decreases and measures of effect size decrease.
A sample of n = 25 scores produces a t statistic of t = -2.062. If the researcher is using a two-tailed test with = .05, the correct statistical decision is:
b. the researcher must fail to reject the null hypothesis with either = .05 or = .01.
A sample of n=16 individuals is selected from a population with y=+80 add a treatment is administered to the sample. After treatment the sample mean m=84 and the sample variance is s2=100. if cohens d is used to measure effect size for this study what value will be obtained for d?
b. 0.40
What is measured by the estimated standard error, SM?
b. How spread out the scores are in the sample.
A sample has a mean of M = 39.5 and a standard deviation of s = 4.3, and produces a t statistic of t = 2.14. For a two-tailed hypothesis test with = .05, what is the correct statistical decision for this sample?
b. It is impossible to make a decision about H0 without more information
A sample of n=25 scores is obtained from a population y=80. which of the following sets of sample statistics will produce the most extreme value for the t statistic?
b. M=90 with s2=10
the estimated standard error, SM, provides a measure of the "average" or standard discrepancy between
b. a sample mean and the population mean (M and y)
A sample of n=15 scores produces a t statistic of t=-.296. If a researcher is using a regular two-tailed test with a=.01, what decision should be made?
b. fail to reject the null hypothesis
With a=.05, the critical values for a two-tailed z-score, test are +1.96. The corresponding values for a two-tailed with a=.05 tend to be_______.
b. greater than +1.96 (farther from zero)
A sample of n = 25 individuals is selected from a population with µ = 80, and a treatment is administered to the sample. Which set of sample characteristics is most likely to lead to a decision that there is a significant treatment effect?
b. m= 90 and small sample variance
With = .05, what is the critical t value for a one-tailed test with n = 25?
b. t= 1.711
As the sample size increases, what happens to the critical values for t? (Assume that the alpha level and all other factors remain constant.)
b. the value decreases
A researcher reports a t statistic with df=20. based on this information, how many individuals were in this sample?
c. 21
The results of a hypothesis test are reported as follows: t(29) = 2.70, p < .05. Based on this report, how many individuals were in the sample?
c. 30
A sample n=4 individuals is obtained from a population with y=80. which set of sample statistics produce the most extreme value for it?
c. M=88 and s2=8
With a=.05 the two-tailed critical region for a sample of n=10 participants would have boundaries of________.
c. t=+2.262
On average, what value is expected for the t statistic when the null hypothesis is true?
d. 0
A sample of n=9 scores has a mean of m=46 and a variance of s2=36. what is the estimated standard error for this sample?
d. 2
To calculate a t statistic, what information is needed from the sample?
d. The t statistic requires the sample variance as well as M and n. (all of the above options are needed to compute t)
holding everything else constant, increasing sample size
d. all of the other options are consequences of increasing sample size
What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72?
d. s2 = 9 and sM = 1
A sample n=25 scores has a mean of M=40 and a variance of s2=100. If this sample is being used to test a null hypothesis stating that y=43, then what is the t statistic for the sample?
d. t=-3/2=-1.50
T OR F: The larger the value for df, the more a t-distribution resembles a normal distribution
true
