Hypotheses for testing for differences between means in two conditions

Question 1

What is the null hypothesis when testing for differences between means in two conditions?

Answer 1

There would be no differences between means in the two conditions

(mean A - mean B = 0)

Question 2

When sample mean B is larger than sample mean A, will the sample mean differences become negative or positive?

Answer 2

Negative

Question 3

When sample mean B is smaller than sample mean A, will the sample mean differences become negative or positive?

Answer 3

Positive

Question 4

What is the formula for sample mean difference?

Answer 4

D = mean A - mean B

Question 5

What are the formulas (2) for the conditional probability of getting the observed sample mean difference mD, assuming the null is true?

Answer 5

1) z = (sample mean diff - pop. mean diff) / pop. s.d.

2) t = (sample mean diff - pop. mean diff) / sample s.d.

Question 6

What are the two types of t-test for assessing differences in means for 2 conditions?

Answer 6

1) Related (or paired or repeated measures) t-test

2) Independent t-test

Question 7

When is the related (or paired or repeated measures) t-test used?

Answer 7

When participants take part in both conditions (WITHIN PARTICIPANTS DESIGN)

Question 8

When is the independent t-test used?

Answer 8

When participants take part in only one of the two conditions (BETWEEN PARTICIPANTS DESIGN)

Question 9

The research hypothesis:

H1: Left-handed people will be more accurate in a task involving left-handed dart throwing at a target than right-handed people doing the same task

is an appropriate example of a hypothesis for an independent groups t-test to test for a difference between means in 2 conditions

a) True
b) False

Answer 9

a) True

Question 10

Imagine that the population of scores for the accuracy (in mm) of dartboard throws at bullseye follows the distribution N(40, 10) for both left handed and right handed people. You repeatedly take a random sample from both the left and right-handed populations and work out the sample mean difference each time. You generate a histogram of sample mean differences. In theory what value should this distribution be centred on?

a) 40

b) 0

c) 10

d) 80

Answer 10

b) 0

Question 11

The hypothesis:

H1: Left-handed people will be more accurate in a task involving left-handed dart throwing than the population mean accuracy for right-handed people doing the same task

is an appropriate example of a hypothesis for an independent groups t-test to test for a difference between sample means in 2 conditions

a) True
b) False

Answer 11

b) False

Question 12

Imagine data in two conditions (A and B) are normally distributed with known population parameters. If the population mean for condition B is higher than that for condition A then for two samples drawn at random from these populations:

The sample mean from population A is likely to be (higher/lower) than that from population B

The sample mean from population A (can/cannot) be higher than that for population B

Answer 12

1) Lower
2) Can