Question

In: Statistics and Probability

what follows use any of the following tests/procedures: Regression, multiple regression, confidence intervals, one sided T-test...

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: Some people believe that the first born children are more intelligent. Given the data 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

Solutions

Expert Solution

We need to check the claim that the first born children are more intelligent.
Here, the independent variable is the Birth Order and the dependent variable is the FIQ: Full-scale IQ.

We have two independent groups here, those who were born first and second i.e Birth order = 1 and 2
Hence, we will use the independent samples t-test.

mu1 is the mean IQ of children born first and mu2 for born second

Ho: mu1 <= mu2
Ha: mu1 > mu2

We will use the one sided t-test (right-tailed)

I. Correct option: A)

II. We have the following sampling data:

FIQ (Order = 1) FIQ (Order = 2)
96 101
88 93
85 94
97 114
124 113
96 89
87 87
101 103
103 96
127 126

Let's conduct the t-test in Excel or any other software of your choice.

In excel, go to data -> data analysis -> independent sample t-test assuming equal variances -> Select the data -> Click OK

The results are:

t-Test: Two-Sample Assuming Equal Variances
FIQ (Order = 1) FIQ (Order = 2)
Mean 100.4 101.6
Variance 210.2666667 157.3777778
Observations 10 10
Pooled Variance 183.8222222
Hypothesized Mean Difference 0
df 18
t Stat -0.197909774
P(T<=t) one-tail 0.422666778
t Critical one-tail 1.734063607
P(T<=t) two-tail 0.845333556
t Critical two-tail 2.10092204

p-value (one-tailed) = 0.423

We fail to reject the null hypothesis as the p-value > 0.05, the test is deemed to be inconclusive.

Correct option: c. Since P-value is too large the test is inconclusive.

III. Conclusion: B. No, we cannot confirm the assertion.

orchestra answered 1 year ago
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