Question

HC: Head Circumference (cm)	TOTVOL: Total Brain Volume (cm3)
57.2	1079
57.2	1104
57.2	1439
57.2	1029
58.5	1160
57.2	1173
57.2	1067
55.8	1347
56.5	1100
59.2	1204
54.7	1005
53	1035
57.8	1281
56.6	1051
53.1	1034
54.2	963
52.9	1027
56.9	1272
55.3	1079
54.8	1070

Open Brain data. SETUP: It is believed that the larger the head circumference the larger the brain volume should be. 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. 9.30595E-20
• b. 0.304733709
• c. 0.022233887
• d. ​​1.86119E-19
• e. ​​None of these

3. Statistical interpretation

• a. Since P-value is very small we are confident that the average of the first sample is smaller 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.

Answer 1

Claim : larger the head circumference larger the head volume

1. To test above claim we use the Regression method because linear relationship of variables gives the information about the change in one variable due to another variable

H₀ : B=0 Vs H₁ : B not equal to zero

2. Using lm command in R ( lm(y~x)) we fit the regression model here y as a response is total brain volume and x as a regressor is head circumference it gives pvalue for regressor is 0.0222

3. Since given Pvalue is smaller than 0.05 therefore we are confident that slope of regression line is not zero

4. Conclusion for above claim is correct becouse regression coefficient is non zero then there is linear relationship between those two variables

Therefore larger the head circumference is larger the brain volume .....