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.

CCMIDSA: Corpus Collasum Surface Area (cm2)   FIQ: Full-Scale IQ   HC: Head Circumference (cm)   ORDER: Birth Order   PAIR: Pair ID (Genotype)   SEX: Sex (1=Male 2=Female)   TOTSA: Total Surface Area (cm2)   TOTVOL: Total Brain Volume (cm3)   WEIGHT: Body Weight (kg)
8.42   96   57.2   1   6   1   1806.31   1079   61.236
7.44   88   57.2   1   7   1   2018.92   1104   79.38
6.84   85   57.2   1   8   1   2154.67   1439   99.792
6.48   97   57.2   1   9   1   1767.56   1029   81.648
6.43   124   58.5   1   10   1   1971.63   1160   72.576
7.62   101   57.2   2   6   1   1689.6   1173   61.236
6.03   93   57.2   2   7   1   2136.37   1067   83.916
6.59   94   55.8   2   8   1   1966.81   1347   97.524
7.52   114   56.5   2   9   1   1827.92   1100   88.452
7.67   113   59.2   2   10   1   1773.83   1204   79.38
6.08   96   54.7   1   1   2   1913.88   1005   57.607
5.73   87   53   1   2   2   1902.36   1035   64.184
6.22   101   57.8   1   3   2   2264.25   1281   63.958
5.8   103   56.6   1   4   2   1866.99   1051   133.358
7.99   127   53.1   1   5   2   1743.04   1034   62.143
7.99   89   54.2   2   1   2   1684.89   963   58.968
8.76   87   52.9   2   2   2   1860.24   1027   58.514
6.32   103   56.9   2   3   2   2216.4   1272   61.69
6.32   96   55.3   2   4   2   1850.64   1079   107.503
7.6   126   54.8   2   5   2   1709.3   1070   83.009

Answer 1

	Male brain volume	Female brain volume
	1079	1005
	1104	1035
	1439	1281
	1029	1051
	1160	1034
	1173	963
	1067	1027
	1347	1272
	1100	1079
	1204	1070
Mean	1170.2	1081.7
SD	130.3762078	107.72501
n	10	10

Equal variance test:

F = S1^2 / S2^2 = 130.38^2/107.73^2 =1.465

FU​ critical = 4.026

F stat < FU​ critical

So, Equal variance is not rejected

Two tailed t test:

Hypothesis:

Ho: μ1​ ≥ μ2​

Ha: μ1​ < μ2​

Critical value:

df = 18 and α = 0.05

tc

-1.734063607

T.INV(α,df)

If t stat < −1.734, reject H0

Test:

Sp^2

14302.34865

((n1-1)S1^2+(n2-1)S2^2)/(n1+n2-2)

t stat

1.654720291

(X1 bar-X2 bar )/SQRT(Sp*(1/n1 + 1/n2))

t stat = 1.655 ≥ tc ​= −1.734, Do not reject H0

P value :

p

0.94234364

T.DIST(ts,df,TRUE)

p = 0.9423 ≥ 0.05, Since P-value is too large we cannot conclude that female brain is smaller in volume.

Conclusion:

There is not enough evidence to conclude that female brain is smaller in volume.