Personal wealth tends to increase with age as older individuals Have had more opportunities to earn and invest than younger individuals. The following data were obtained from a random sample of eight individuals and record the total wealth (Y) and their Personal wealth tends to increase with age as older individuals current age (X). Person Total wealth(‘000s of dollars) Y Age (Years) X A 280 36 B 450 72 C 250 48 D 320 51 E 470 80 F 250 40 G 330 55 H 430 72 A part of the output of a regression analysis of Y against X using Excel is given below. SUMMARY OUTPUT Regression Statistic Multiple R 0.954704 R Square 0.91146 Adjusted R Square 0.896703 Standard Error 28.98954 Observation 8 df df SS MS F Significant F Regression 1 51907.64 51907.64 Residual 6 5042.361 840.3936 Total 7 56950 Coefficient Standard error T Stat P-value Intercept 45.2159 39.8049 Age 5.3265 0.6777 Test whether there is a significant relationship between wealth and age at the 10% significant level. Perform the test using the following six steps. Step 1. Statement of hypothesis Step2. Standardized test statistic. Step3. Level of Significance Step4. Decision rule Step5. Calculation of test statistic Step6. Conclusion

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Personal wealth tends to increase with age as older individuals

Have had more opportunities to earn and invest than younger individuals. The following data were obtained from a random sample of eight individuals and record the total wealth (Y) and their Personal wealth tends to increase with age as older individuals current age (X).

Person	Total wealth(‘000s of dollars) Y	Age (Years) X
A	280	36
B	450	72
C	250	48
D	320	51
E	470	80
F	250	40
G	330	55
H	430	72

A part of the output of a regression analysis of Y against X using Excel is given below.

SUMMARY OUTPUT

Regression Statistic
Multiple R	0.954704
R Square	0.91146
Adjusted R Square	0.896703
Standard Error	28.98954
Observation	8

df df	SS	MS	F	Significant F
Regression	1	51907.64	51907.64
Residual	6	5042.361	840.3936
Total	7	56950

	Coefficient	Standard error	T Stat	P-value
Intercept	45.2159	39.8049
Age	5.3265	0.6777

Test whether there is a significant relationship between wealth and age at the 10% significant level. Perform the test using the following six steps.

Step 1. Statement of hypothesis

Step2. Standardized test statistic.

Step3. Level of Significance

Step4. Decision rule

Step5. Calculation of test statistic

Step6. Conclusion

Expert Solution

Step 1

The hypotheses can be constructed as:

H₀: β₁ = 0

H₁: β₁ ≠ 0

Step 2

The standardised test statistic can be written as:

Step 3

The level of significance is provided as 10% that is 0.10.

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