Question

Step by step solution and explanation, please?

State whether each of the following data sets has positive or negative linear correlation (or neither). Also calculate the correlation coefficient using the Five steps for Hypothesis testing. The global average temperature (in degrees Celsius), and number of pirates are:

Temperature	14.2	14.4	14.5	14.8	15.1	15.5	15.8
Pirates	35000	45000	20000	15000	5000	400	17

Answer 1

	X	Y	X*Y	X2	Y2
	14.2	35000	497000	201.64	1225000000
	14.4	45000	648000	207.36	2025000000
	14.5	20000	290000	210.25	400000000
	14.8	15000	222000	219.04	225000000
	15.1	5000	75500	228.01	25000000
	15.5	400	6200	240.25	160000
	15.8	17	268.6	249.64	289
Sum =	104.3	120417	1738968.6	1556.19	3900160289

based on the data provided, we get that

Therefore, based on this information, the sample correlation coefficient is computed as follows

Thus , the given data set has negative linear correlation.

Hypothesis Testing:

1.Null and alternative hypothesis:

2. Set level of significance

3. Rejection region:

The sample size is n = 7, so then the number of degrees of freedom is df = n-2 = 7 - 2 = 5

The corresponding critical t value t_c​ for a significance level of α=0.05, for a left-tailed test is:.

Reject H0 if .

4. Test Statistic:

5. Decision: Since t=-4.2952 < tc=-2.015, it is concluded that the null hypothesis is rejected at 5% level of significance.

i.e. There is negative linear correlation between the global average temperature (in degrees Celsius), and number of pirates.