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

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 word**s 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 r^{2} to measure the size of the treatment
effect.

r^{2} 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
word**s 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 r^{2} to measure the
size of the treatment effect.

Since r^{2} > 0.25 , it has large effect.

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