Question

Research Question: Does the spatial ability differ by biological sex?
(Use Data A)

Null Hypothesis: Spatial ability does not differ by biological sex.

1. What is the statistic and its formula to address this research question? [1pt]

	Female	Male
X bar	76.2	80.5
s	12.82	11.40
n	10	10

4. Calculate the t-value? [2 pt]

5. What is the critical value if alpha = 0.05 for two-tailed test? [2 pt]

6. Do we reject or accept the null hypothesis?  

7. What is the effect size (Cohen’s d)? [1 pt]

Data A: Students’ Spatial Ability

ID	Biological Sex	Spatial Ability
	1= female; 0=male
1	1	80
2	0	70
3	1	60
4	0	65
5	1	80
6	1	76
7	1	89
8	1	64
9	1	66
10	1	99
11	1	85
12	1	63
13	0	97
14	0	94
15	0	83
16	0	79
17	0	72
18	0	68
19	0	88
20	0	89

Answer 1

Given that,
mean(x)=76.2
standard deviation , s.d1=12.82
number(n1)=10
y(mean)=80.5
standard deviation, s.d2 =11.4
number(n2)=10
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.262
since our test is two-tailed
reject Ho, if to < -2.262 OR if to > 2.262
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =76.2-80.5/sqrt((164.3524/10)+(129.96/10))
to =-0.793
| to | =0.793
critical value
the value of |t α| with min (n1-1, n2-1) i.e 9 d.f is 2.262
we got |to| = 0.79262 & | t α | = 2.262
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -0.7926 ) = 0.448
hence value of p0.05 < 0.448,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
D.
test statistic: -0.793
E.
critical value: -2.262 , 2.262
F.
decision: do not reject Ho
p-value: 0.448
we do not have enough evidence to support the claim that the spatial ability differ by biological sex.
G.
cohens d size =( mean 1 -mean 2)/ standard deviation pooled
standard deviation pooled = sqrt((sd1^2 +sd 2^2)/2)
standard deviation pooled = sqrt((12.82^2 +11.40^2)/2) = 12.1307
cohens d size =( mean 2-mean 1)/ standard deviation pooled
cohens d size =( 80.5-76.2)/ 12.130
cohens d size = 0.354