Question

In what follows use any of the following tests: Regression, multiple regression, one-sided t-test, or two-sided t-test. All conclusions should be based on 5% P-value threshold.

Choose the best fitting answer.

Open Brains data. SETUP: Since females are on average smaller than males, some people believe that female brains should be smaller as well (smaller volume). Given the data, your job is to perform the appropriate statistical test or procedure and help them decide.

5. What test did you perform?

• a. Regression
• b. ​​Multiple regression
• c. One-sided t-test
• d. ​​Two-sided t-test

6. What is the P-value?

• a. 0.115912154
• b. 0.057956077
• c. 7.38553E-20
• d. 3.69277E-20
• e. None of these

7. What is the Statistical interpretation?

• a. Since P-value is very small we can conclude that female brain is smaller in volume.
• b. Since P-value is too large we cannot conclude that male and female brains have different volume.
• c. Since P-value is too large we cannot conclude that female brain is smaller in volume.
• d. None of these.

8. What is the conclusion?

• a. Test is inconclusive; thus nothing can be concluded.
• b. Test is inconclusive; thus we cannot claim that the brain volumes are different.
• c. Test is inconclusive; thus we cannot claim that there is a correlation between brain volume and gender.
• d. None of these.

SEX: Sex (1=Male 2=Female)	TOTVOL: Total Brain Volume (cm3)
1	1079
1	1104
1	1439
1	1029
1	1160
1	1173
1	1067
1	1347
1	1100
1	1204
2	1005
2	1035
2	1281
2	1051
2	1034
2	963
2	1027
2	1272
2	1079
2	1070

Answer 1

5)

c. One-sided t-test (since we are testing if female has smaller brain size)

6)

from excel :data-data analysis: T -test

t-Test: Two-Sample Assuming Equal Variances
	male	female
Mean	1170.2	1081.7
Variance	16997.96	11604.68
Observations	10	10
Pooled Variance	14301.32
Hypothesized Mean Difference	0
df	18
t Stat	1.65478
P(T<=t) one-tail	0.05765
t Critical one-tail	1.734064
P(T<=t) two-tail	0.1153
t Critical two-tail	2.100922

b. 0.057956077

7)

c. Since P-value is too large we cannot conclude that female brain is smaller in volume.

8)

a. Test is inconclusive; thus nothing can be concluded.