Question

In what follows use any of the following tests/procedures: Regression, multiple regression, confidence intervals, one sided T-test or two sided T-test. All the procedures should be done with 5% P-value or 95% confidence interval.Some answers are approximated, choose the most appropriate answer. Open Brains data. SETUP: Are the IQ’s for male and female subjects different? Given your job is to confirm or disprove this assertion.

I. What test/procedure did you perform? (6.66 points)

• a. One sided T-test
• b. Two sided T-test
• c. Regression
• d. Confidence interval

II. Statistical interpretation? (6.66 points)

• a. Since P-value is small we are confident that the slope is not zero.
• b. Since P-value is small we are confident that the averages are different.
• c. Since P-value is too large the test is inconclusive.
• d. None of these.

III. Conclusion? (6.66 points)

• a. Yes, we can confirm the assertion.
• b. No, we cannot confirm the assertion.

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

R-commands and output:

# Assertion: The IQ’s for male and female subjects are different.

# I. What test/procedure did you perform?
# b. Two sided T-test
# Null Hypothesis-H0: The IQ’s for male and female subjects are SAME.
# Vs Alternative Hypothesis-H1: The IQ’s for male and female subjects are DIFFERENT.
# To test above hypotheses, we test means and give general conclusion
# Thus, Mathematically, we can write,
# H0: mean IQ of males (muM) = mean IQ of females (muF)
# Vs H1: (muM) not equal to (muF)
# We use R-Software as follows:

d=scan("clipboard")
d
IQ=c(96,88,85,97,124,101,93,94,114,113,96,87,101,103,127,89,87,103,96,126)
sex=c(1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2)
table(sex)
sex
1 2
10 10
# count of female= count of male =10
male=IQ[1:10]
female=IQ[11:20]

# Test statistic is:
xbar=mean(male)
ybar=mean(female)
xv=var(male)
xv
[1] 157.6111
yv=var(female)
yv
[1] 210.2778
nM=length(male)
nF=length(female)
t=(xbar-ybar)/sqrt(xv/nM+yv/nF)
t
[1] -0.16487

# By direct command in R
> t.test(male,female,paired=FALSE)
Welch Two Sample t-test
data: male and female
t = -0.16487, df = 17.639, p-value = 0.8709
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-13.76165 11.76165
sample estimates:
mean of x mean of y
100.5 101.5
# From the output, we have p-value=0.8709. Here, p-value is greater than alpha=0.05, hence we fail to Reject H0.

# II. Statistical Interpretation
# d. None of these.
# Since p-value > alpha, we say that mean (or average) IQs of males and females are Same.

# III. Conclusion
# b. No, we cannot confirm assertion.