Question

HWB4-DueApril26 (1)-Saved to my Mac Rohwedder and Willis (2010) gave memory tests to people aged 60 to 64 years in some European and North American countries. Their results suggested that early retirement may lead to memory decline. 7. The table shows some of their data (NOTE: a greater Percent Retired means that more people retired younger). Percent Retired Memory Score Country Sweden USA 39 48 59 70 74 78 81 87 9.3 10.9 10.7 9.1 6.4 9.1 7.2 England Germany Spain Netherlands Italy France Belgium Austria 7.9 8.5 9.0 าร 91 Use the four-step process to explain your analysis. Write up the results using APA format. a. b. MacBook Air

Answer 1

(a)

Hypotheses are:

$H_{0}:\rho=0$

$H_{a}:\rho\neq 0$

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	39	9.3	1521	86.49	362.7
	48	10.9	2304	118.81	523.2
	59	10.7	3481	114.49	631.3
	70	9.1	4900	82.81	637
	74	6.4	5476	40.96	473.6
	78	9.1	6084	82.81	709.8
	81	7.2	6561	51.84	583.2
	87	7.9	7569	62.41	687.3
	88	8.5	7744	72.25	748
	91	9	8281	81	819
Total	715	88.1	53921	793.87	6175.1

Sample size: n=10

Now,

$S_{yy}=\sum y^{2}-\frac{\left (\sum y \right )^{2}}{n}=17.709$

$S_{xx}=\sum x^{2}-\frac{\left (\sum x \right )^{2}}{n}=2798.5$

$S_{xy}=\sum xy-\frac{\left (\sum x \right )\left (\sum y \right )}{n}=-124.05$

The coeffcient of correlation is :

$r=\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=-0.557$

Test statistics:

$t=\frac{r}{\sqrt{\frac{1}{n-2}(1-r^{2})}}=-1.897$

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Here degree of freedom is df=n-2=8 so p-value of the test is 0.0944.

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Because the P-value is gereater than the significance level 0.05, there is not sufficient evidence to support the claim that there is a linear correlation between the variables.

b)

t(8) = -1.897, p > 0.05