Question

The correlation coefficient *r* is a sample statistic.
What does it tell us about the value of the population correlation
coefficient *ρ* (Greek letter rho)? You do not know how to
build the formal structure of hypothesis tests of *ρ* yet.
However, there is a quick way to determine if the sample evidence
based on *ρ* is strong enough to conclude that there is some
population correlation between the variables. In other words, we
can use the value of *r* to determine if *ρ* ≠ 0. We
do this by comparing the value |*r*| to an entry in the
correlation table. The value of *α* in the table gives us
the probability of concluding that *ρ* ≠ 0 when, in fact,
*ρ* = 0 and there is no population correlation. We have two
choices for *α*: *α* = 0.05 or *α* = 0.01.

1. Look at the data below regarding the variables *x* =
age of a Shetland pony and *y* = weight of that pony. Is the
value of |*r*| large enough to conclude that weight and age
of Shetland ponies are correlated? Use *α* = 0.05. (Use 3
decimal places.)

x |
3 | 6 | 12 | 18 | 26 |

y |
60 | 95 | 140 | 182 | 178 |

(a) r |
= |

(b) critical r |
= |

2. Conclusion

(A) Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.

(B) Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated.

(C) Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated.

(D) Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.

3. Look at the data below regarding the variables *x* =
lowest barometric pressure as a cyclone approaches and *y* =
maximum wind speed of the cyclone. Is the value of |*r*|
large enough to conclude that lowest barometric pressure and wind
speed of a cyclone are correlated? Use *α* = 0.01. (Use 3
decimal places.)

x |
1004 | 975 | 992 | 935 | 970 | 934 |

y |
40 | 100 | 65 | 145 | 69 | 148 |

r |
= |

critical r |
= |

4. Conclusion

(A) Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

(B) Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

(C) Fail to reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

(D) Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

Answer #1

1)

a)

correlation r='Sxy/(√Sxx*Syy) = |
0.926 |

b)

critical r =0.878 (please try 0.88 if this comes wrong)

2)

(A) Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.

3)

correlation r='Sxy/(√Sxx*Syy) = | -0.958 |

critical r =0.917 (please try 0.92 if this comes wrong)

4)

(A) Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

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