Chapter 9: Introduction to the t Statistic

more information than the researcher typically has available

(population standard deviation)

The problem with z score testing is that the formula require...

t statistic

an alternative to z that does not require known population variance (standard deviation)

estimated standard error

is used as an estimate of the real standard error when the value of σm is unknown

t family of distributions

approximates the shape of the normal distribution

-flatter than the normal distrubtion

-more spread out than the normal distribution

-more variabilty (fatter tails)

-values in the sample are independent

-with population sampled must be normal

Assumptions for the t test are:

B. is flatter and more spread out than the normal z distribution

When n is small (less than 30), the t distribution ______________.

A. is almost identical in shape to the normal z distribution

B. is flatter and more spread out than the normal z distribution

C. is taller and narrower than the normal z distribution

D. cannot be specified, making hypothesis tests impossible

True

All elements of the t statistic will be the same for each sample

By chance, two samples selected from the same population have the same size (n=36) and the same mean (M=83). They will also have the same t statistic.

True

False

True

The t statistic does not require the population standard deviation; the z-test does

Compared to a z-score, a hypothesis with a t statistic requires less information about the population

True

False

greater than chance

Hypothesis test determines whether the treatment effect is

statistically significant

A very small treatment effect can be

measure of effect size

Cohen's d is a measure of

two or non directional

In most cases a t test will have how many tails?

False

Measures of effect size are not influenced to any great extent by sample size

Sample size has a great influence on measures of effect size

True or False

False

When the value of t is near 0, the difference between M and mu is also near 0

When the value of the t statistic is near 0, the null hypothesis should be rejected.

b. the average distance between a sample mean and the population mean

What is measured by the estimated standard error, sM?

a. how spread out the scores are in the sample

b. the average distance between a sample mean and the population mean

c. how spread out the scores are in the population

d. the average distance between a score and the sample mean

d. a large sample size and a small sample variance

Which set of characteristics will produce the smallest value for the estimated standard error?

a. a small sample size and a large sample variance

b. a small sample size and a small sample variance

c. a large sample size and a large sample variance

d. a large sample size and a small sample variance

b. M = 90 and small sample variance

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?

a. M = 90 and large sample variance

b. M = 90 and small sample variance

c. M = 85 and small sample variance

d. M = 85 and large sample variance

a. n = 36

A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 35, how many individuals were in the sample?

a. n = 36

b. n = 35

c. n = 34

d. cannot be determined from the information given

b. All of the other options are true as sample size increases.

As sample size increases _______.

a. the value of df also increases

b. All of the other options are true as sample size increases.

c. the critical values of t move closer to zero.

d. the t distribution becomes more like a normal distribution

C. The t statistic is used when the population variance (or standard deviation) is unknown

In what circumstances is the t statistic used instead of a z-score for a hypothesis test?

A. The t statistic is used when the sample size is n=30 or larger

B. The t statistic is used when the population mean is unknown

C. The t statisti is used when the population variance (or standard deviation) is unknown

D. The t statistic is used if you are not sure that the population distribution is normal

A. 0

when the null is true it should equal 0

On average, what value is expected for the t statistic when the null hypothesis is true?

A. 0

B. 1

C. 1.96

D. t> 1.96

A. Small variance for a large sample

A sample is selected from a population and a treatment is administered to the sample. For a hypothesis test with a t statistic, if there is a 5-point difference between the sample mean and the original population mean, which set of sample characteristics is most likely to lead to a decision that there is a significant treatment effect?

A. small variance for a large sample

B. small variance for a small sample

C. large variance for a large sample

D. large variance for a small sample

D. All three samples would produce the same value for Cohen's d.

Sample size is irrelevant to Cohen's d

A sample is selected from a population with a mean of 75, and a treatment is administered to the individuals in the sample. The researcher intends to use a t statistic to evaluate the effect of the treatment. If the sample mean is M=79, then which of the following outcomes would produce the largest value for Cohen's d?

A. n=4 and s^2=30

B. n=16 and s^2=30

C. n=25 and s^2=30

D. All three samples would produce the same value for Cohen's d.

B. t(24)=2.15, p<0.05

(alligator mouth must eat the alpha level in a significant result)

A researcher uses a sample of n=25 individuals to evaluate the effect of a treatment. The hypothesis test uses a=.05 and produces a significant result with t=2.15. How would this result be reported in the literature?

A. t(25)=2.15, p<0.05

B. t(24)=2.15, p<0.05

C. t(25)=2.15, p> 0.05

D. t(24)=2.15, p>0.05

A. mean is less than or equal to 30

A sample is selected from a population with a mean of 30 and a treatment is administered to the sample. If the treatment is expected to increase scores and a t statistic is used for a one-tailed hypothesis test, then which of the following is the correct null hypothesis?

A. mean is less than or equal to 30

B. mean is <30

C. mean is greater than or equal to 30

D. mean is >30

D. Possibly reject the null hypothesis if the treatment effect is in the predicted direction

A researcher fails to reject the null hypothesis with a regular two tailed test using alpha=.05. If the researcher used a directional (one-tailed) test with the same data and the same alpha level, then what decision would be made?

A. Definitely reject the null hypothesis

B. Definitely reject the null hypothesis if the treatment effect is in the predicted direction

C. Definitely fail to reject the null hypothesis

D. Possibly reject the null hypothesis if the treatment effect is in the predicted direction