Question

In what follows use any of the following tests/procedures: 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.

Open Brain data. SETUP: It is believed that the person whose brain has larger surface area (i.e. TOTSA: Total Surface Area) that the person will have the larger brain volume as well. Given the data your job is to confirm or disprove this assertion.

1. What test/procedure did you perform?

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

2. What is the P-value/margin of error?

• a. 0.248605264
• b. 0.005070081
• c. 3.44547E-20
• d. 5.27739E-08
• e. ​​None of these

3. Statistical interpretation

• a. Since P-value is very large we cannot confirm that the average of the first sample is larger than the other.
• b. Since P-value is very small we are very confident that the averages are different.
• c. Since P-value is very small we are confident that the slope of regression line is not zero.
• d. ​​None of these.

4. Conclusion

• a. Yes, I am confident that the above assertion is correct.
• b. No, we cannot claim that the above assertion is correct.

paste content below in a text document and then open the text document with excel

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

1)

Answer: C. Regression

Explanation: Since we want test whether the larger brain surface are is positively correlated with the larger brain volume such that person whose brain has larger surface area will have the larger brain volume as well, the regression analysis will be used.

2)

Answer: b. 0.005070081

Explanation:

The regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'TOTVOL' column, Input X Range: 'TOTSA' column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The hypothesis is tested by calculating t-value and corresponding p-value for the estimated slope in regression model as shown below,

Null Hypothesis:

Alternate Hypothesis:

The P-value is obtained in regression analysis

	P-value
TOTSA: Total Surface Area (cm2)	0.00507

3)

Answer: c. Since P-value is very small we are confident that the slope of regression line is not zero.

Explanation:

Since the P-value = 0.00507 < 0.05 at 5% significant level, the null hypothesis is not rejected hence there is sufficient evidence that slope slope of regression line is not zero.

4)

Conclusion: a. Yes, I am confident that the above assertion is correct.