Question

In: Statistics and Probability

DETROIT (Y) ANN ARBOR (X) 2008 59 2008

DETROIT (Y) ANN ARBOR (X)

2008 59 2008 61

2009 60 2009 58

2010 61 2010 60

2011 69 2011 68

2012 66 2012 67

2013 62 2013 64

2014 64 2014 66

2015 71 2015 70

2016 69 2016 72

2017 66 2017 64

h₀:There is a statistical correlation between the temperatures in two different Michigan cities.

What relationships exist between the data sets? Are they significant and why?

Expert Solution

Here we are to test the presense of correlation between the temperatures of two different Michigan cities.

If be the correlation coefficient between the temperatures of the two cities.

We are to test the hypothesis :

versus

If r be the sample correlation coeffecient and n be the sample size which is 10.

The appropriate test statistic would be :

Now, t follows t-distribution with (n-2) degrees of freedom.

We shall reject our null hypothesis if our observed t > t_;n-2

Our sample correlation r=0.906788 from which we may conclude that linear relationship exists between the data sets.

Accordingly, t=0.906788 * sqrt(10-2) / sqrt(1-0.906788²)

= 6.0836

If our chosen level of significance

t_0.05,8 =1.860

Clearly , Observed t > t_0.05,8

So, we reject our null hypothesis at 5% level of significance and conclude that the temperature in the two cities are significantly correlated.

orchestra answered 2 years ago

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