A cognitive psychologist wanted to test the effects of priming a participant with either telling them that the "task they were about take was easy" or the "task they were about to take was difficult" and how this affected responses assuming that when participants with were primed with the "hard" condition, performance would decrease. Twenty participants had both conditions presented to them some with "easy" condition first and some with the "hard" condition first. The following is the mean of the difference scores for the two tasks MD=8 and an SEM=2.8

a. State the null and alternative hypotheses
b. Perform a paired samples t test with the descriptive statistics
c. Is there a significant difference between the two conditions?
Test using an alpha level of .05, using the direction of the test that is listed in the question.
Use APA format in answering question.

At a significance level of .05, there is enough evidence to support the claim that the effects of priming a participant affect the outcome significantly.

Step-by-step explanation:

This is a paired samples t-test for the population mean difference.

The claim is that the effects of priming a participant affect the outcome significantly.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_d=0\\\\H_a:\mu_d> 0[/tex]

The significance level is .05.

The sample has a size N=20.

The sample mean difference is MD=8.

The standard error of the mean is SEM=2.8.

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{8-0}{2.8}=\dfrac{8}{2.8}=2.857[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=20-1=19[/tex]

This test is a right-tailed test, with 19 degrees of freedom and t=2.857, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>2.857)=0.005[/tex]

As the P-value (.005) is smaller than the significance level (.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the effects of priming a participant affect the outcome significantly.