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.

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