Question

A researcher used a sample of n= 25 adults between the ages of 40 and 45. For each person, the researcher recorded the difference between the ratings obtained while smiling and the rating obtained while frowning. On average the cartoons were rated as funnier when the participants were smiling, with an average difference of M_D = 1.6, with SS = 150.

Are the cartoons rated as significantly funnier when the participants are smiling ? Use a one-tailed test with α = .01.

a)The alternative hypothesis in words is:

b)The null hypothesis in symbols is:

c)The critical t-value is (Note: Include all the numbers after the decimal point.)

d)The t-statistic is:

e)Your decision is:

f)Compute r² to measure the size of the treatment effect.

r² is :

Answer 1

Solution:

Given:

Sample size = n = 25

an average difference of M_D = 1.6

SS = 150.

one-tailed test with α = 0.01.

Are the cartoons rated as significantly funnier when the participants are smiling ?

Part a) The alternative hypothesis in words is:

The cartoons rated as significantly funnier when the participants are smiling.

Part b)The null hypothesis in symbols is:

Part c)The critical t-value is

df = n - 1 = 25 -1 = 24

One tail area = 0.01

t critical value = 2.492

Part d)The t-statistic is:

thus

Part e)Your decision is:

Since t test statistic value = 3.200 > t critical value = 2.492, we reject null hypothesis H0.

Part f)Compute r² to measure the size of the treatment effect.

Since r² > 0.25 , it has large effect.