Question

1. 3 e) Of course the number of years smoked and longevity do not follow a normal distribution. That being the case, we have to use a nonparametric test to test if there is a correlation between these two variables. So using the Spearman correlation approach, test the claim at 95% confidence that there is a negative correlation between these two variables.
   1. State the Null and Alternative Hypothesis (1)
   2. Draw the appropriate probability density curve setting up the problem and state the Decision Rule. (1)
   3. Determine the Spearman Correlation Coefficient (2)
   4. Perform the test (2)
   5. State your decision (1)
      
      (Note, to help you out, I have started your Spearman calculation)
      

	Years Smoked	Rank Value	Age at Death of Participant	Rank Value	d	d2
	5		81
	23		76
	48		53
	8		84
	4		79
	26		74
	11		83
	19		75
	14		72
	35		71
	4		92
	23		65
Totals		78		78	0

Answer 1

State the Null and Alternative Hypothesis (1)

Ans: The Null Hypothesis H₀: r=0

Vs H₁: r < 0

Draw the appropriate probability density curve setting up the problem and state the Decision Rule. (1)

Determine the Spearman Correlation Coefficient (2)

Ans please follow picture attached

		Rank Value	Age at Death of Participant	Rank Value	d	d2
	Years Smoked
	5	10	81	4	6	36
	23	4.5	76	6	-1.5	2.25
	48	1	53	12	-11	121
	8	9	84	2	7	49
	4	11.5	79	5	6.5	42.25
	26	3	74	8	-5	25
	11	8	83	3	5	25
	19	6	75	7	-1	1
	14	7	72	9	-2	4
	35	2	71	10	-8	64
	4	11.5	92	1	10.5	110.25
	23	4.5	65	11	-6.5	42.25
Totals		78		78	0	522
	r=	-0.82867

Perform the test (2)

Calculation of z as follows

Ans

Tabulated at 5% level of significance

State your decision (1)

Ans We will reject our null hypothesis H₀ and Accept the alternative hypothesis H₁