Question

A researcher compared happiness level between a group of people who watched and a group of those who did not watch the FIFA World Cup in 2018. The following scores were obtained for each group;

Watched: 10 8 7 9 13 7 6 12

Did not watch: 7 4 9 3 7 6 10 2

The question is;

Are the scores significantly lower for the group that did not watch the FIFA World Cup? Test at Alpha level of .05

In your answer, clearly state the following;

Hypotheses, assumptions required for independent t-test, degrees of freedom, critical value, obtained value (show every step of your calculations) and your conclusion.

Answer 1

Ans:

	watched	did not watch
1	10	7
2	8	4
3	7	9
4	9	3
5	13	7
6	7	6
7	6	10
8	12	2
mean=	9	6
std. dev=	2.51	2.83

Assumption:Both populations have equal variances.

pooled standard deviation=sqrt(((8-1)*2.51^2+(8-1)*2.83^2)/(8+8-2))=2.673

standard error for difference=2.673*sqrt((1/8)+(1/8))=1.336

Test statistic:

t=(9-6)/1.336

t=2.245

df=8+8-2=14

p-value=tdist(2.245,14,1)=0.0207

critical t value(right tailed)=1.761

As,t=2.245 is greater than critical t value,we reject the null hypothesis.

There is sufficient evidence to conclude that the scores significantly lower for the group that did not watch the FIFA World Cup