PSYC*1010 Chapter 9: Intro to the t Statistic

Question 1

When are t statistics used as a replacement for z-scores?

Answer 1

When the population standard deviation/variance is unknown

Question 2

T or F: z-tests are more versatile than t-tests.

Answer 2

False. t-tests are more versatile.

Question 3

When is estimated standard error used?

Answer 3

When population standard deviation/variance is unknown

Question 4

What does the estimated standard error provide a measurement of?

Answer 4

An estimate of the standard distance between the sample mean and the population mean

Question 5

How is estimated standard error denoted?

Answer 5

s (subscript M)

Question 6

What is the difference between the t statistic formula and the z-score formula?

Answer 6

The structure is the same, but the t formula uses the notation for sample data rather than population parameters

Question 7

What are degrees of freedom?

Answer 7

The number of scores in a sample that are independent and free to vary

Question 8

Does an increase in degrees of freedom indicate an increase or a decrease in the sample’s ability to represent the population?

Answer 8

Increase

Question 9

T or F: The greater the value of degrees of freedom, the better t will approximate the z-score.

Answer 9

True

Question 10

What is a t distribution?

Answer 10

The complete set of t values computed for every possible random sample of a specific size

Question 11

What determines how well a t distribution approximates a normal distribution?

Answer 11

Degrees of freedom/sample size

Question 12

The distribution of sample means will create an almost perfectly normal distribution if one of what two criteria are met?

Answer 12

• n>30
• The samples were selected from a normal population

Question 13

T or F: There is a different sampling distribution of t for each possible number of degrees of freedom.

Answer 13

True

Question 14

Does the t distribution have more or less variability than a z-score distribution?

Answer 14

More

Question 15

How do the shapes of a t distribution and normal z distribution tend to differ?

Answer 15

The t distribution tends to be flatter and more spread out, and a normal z distribution has more of a central peak

Question 16

What is the main reason for the shape disparity in z and t distribution?

Answer 16

In the z formula, only the numerator varies between samples (denominator uses population parameters which are consistent for all sample sizes), but for the t formula both the numerator and denominator vary

Question 17

What does it mean for t tables to be abridged?

Answer 17

They don’t include entries for every possible df value

Question 18

How is the t value determined if the degrees of freedom aren’t listed in the table?

Answer 18

Look up the critical t for both surrounding values and use the larger value for t

Question 19

What is a t statistic?

Answer 19

The difference between the sample mean (from data) and the population mean (hypothesized from H0), divided by the estimated standard error

Question 20

What is the conclusion of a hypothesis test if the t statistic is larger (+ or -) than expected if H0 was true?

Answer 20

H0 is rejected

Question 21

What is the conclusion of a hypothesis test if the t statistic is smaller (+ or -) than expected if H0 was true?

Answer 21

H0 fails to be rejected

Question 22

What is the unknown population?

Answer 22

The population that exists after the treatment is administered

Question 23

How is the null hypothesis obtained in a t test?

Answer 23

A theory, logical prediction, or simply wishful thinking

Question 24

What are the two assumptions of a t test?

Answer 24

• The values in the sample consist of independent observations
• The population sampled is normal (or n>30)

Question 25

What does it mean for two observations to be independent of each other?

Answer 25

If the occurrence of one has no effect on the probability of the second

Question 26

T or F: The sample size and magnitude of variability both have a large effect on the t statistic.

Answer 26

True

Question 27

Will a larger standard error produce a larger or smaller t statistic?

Answer 27

Smaller

Question 28

What two factors determine the magnitude of standard error?

Answer 28

• Sample size
• Sample variance

Question 29

Will a larger sample produce a larger or smaller standard error?

Answer 29

Smaller

Question 30

Will a larger variance produce a larger or smaller standard error

Answer 30

Larger

Question 31

Does an increase in percentage of confidence increase or decrease the value of t?

Answer 31

Increase

Question 32

How does the size of a sample influence the confidence interval?

Answer 32

The bigger the sample, the smaller the interval

Question 33

What are the two types of t tests?

Answer 33

• Independent-measures t-test (between subjects design)
• Repeated-measures t-test (within subjects design)