Question

In what follows use any of the following tests/procedures: Regression, multiple regressions, 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.

Upload the data HeartRate_Exercise. These data are based on 45 randomly chosen high school students.

SETUP: Is it reasonable to claim that students who exercise more have lower heart beat rate at rest. Given the data your job is to confirm or disprove this claim.

5. What test/procedure did you perform?

a. One-sided t-test

b. Two-sided t-test

c. Regression

d. Confidence interval

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

a. 1.56075E-45

b. 3.1215E-45

c. 6.149555

d. 0.014702

e. None of these

7. Statistical Interpretation

a. Since the P-value is very small, we are confident that the average heart rate is above 70.

b. Since the P-value is very small, we are very confident that the averages are different.

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

d. We are 95% certain that the confidence interval is [72.18, 84.48].

e. None of these

8. Conclusion

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

b. No, we cannot claim that the above assertion is correct.

weekly exercise (hours) Heart Rate at rest
16      55
2       76
3       78
17      46
19      76
3       68
19      61
12      68
15      48
2       71
4       72
2       81
10      64
9       61
0       73
0       84
5       72
16      58
0       77
19      54
4       79
8       73
6       85
17      57
2       75
7       85
13      73
3       75
8       84
6       52
5       60
18      69
1       66
19      90
19      64
5       65
0       74
2       55
18      67
2       78
0       71
18      76
11      76
13      84
0       91

Answer 1

5. Test performed = Regression.

6.

Ʃ x =	378
Ʃ y =	3167
Ʃ xy =	25395
Ʃ x² =	5284
Ʃ y² =	228181
Sample size, n =	45
x̅ = Ʃx/n =	8.4
y̅ = Ʃy/n =	70.3778
SSxx = Ʃx² - (Ʃx)²/n =	2108.8
SSyy = Ʃy² - (Ʃy)²/n =	5294.58
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	-1207.8

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = -0.3615

Null and alternative hypothesis:      
Ho: ρ = 0 ; Ha: ρ ≠ 0  

α =    0.05  

Test statistic :    

t = r*√(n-2)/√(1-r²) = -2.5421

df = n-2 = 43

p-value = T.DIST.2T(ABS(-2.5421), 43) = 0.014702

Answer D.  

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

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