Question

An investment advisor claimed that the return to Bitcoin is 4% while the returns to other three shares are no different from zero. Do you agree? Justify your reasoning using a two-tailed hypothesis test approach at the significance level of 5%.

Bitcoin
Mean	1.566281492
Standard Error	1.019391171
Median	1.425067488
Mode	#N/A
Standard Deviation	14.7723815
Sample Variance	218.2232553
Kurtosis	11.72022419
Skewness	-1.075057651
Range	165.6816869
Minimum	-100
Maximum	65.68168686
Sum	328.9191133
Count	210
TLS Mean -0.7385425 Standard Error 0.50800517 Median -0.17398 Mode 0 Standard Deviation 7.36169432 Sample Variance 54.1945432 Kurtosis 159.781158 Skewness -11.836209 Range 107.894737 Minimum -100 Maximum 7.89473684 Sum -155.09393 Count 210 BHP Mean -0.399923172 Standard Error 0.564401885 Median -0.234980011 Mode #N/A Standard Deviation 8.178960351 Sample Variance 66.89539242 Kurtosis 105.6649434 Skewness -8.574422353 Range 119.1594623 Minimum -100 Maximum 19.1594623 Sum -83.9838661 Count 210 CBA Mean -0.514242394 Standard Error 0.507107254 Median 0.104494399 Mode #N/A Standard Deviation 7.348682261 Sample Variance 54.00313098 Kurtosis 162.4049611 Skewness -11.97272186 Range 107.0984119 Minimum -100 Maximum 7.098411947 Sum -107.9909028 Count 210

Answer 1

First for bitcoin :

Null Hypothesis : H₀ : = 4%

Alternative Hypothesis : H_a : 4%

Test statistic

t = (1.566281492 - 4)/1.019391171 = -2.387

Here for degree of freedom = 210 - 1 = 209

and 0.05 signficance level

t_critical = 1.9714

Here l t l > t_critical so we reject the null hypothesis and conclude that return in bitcoin is not 4%.

now for stock 1 TLS

Null Hypothesis : H₀ : = 0%

Alternative Hypothesis : H_a : 0%

Test statistic

t = (-0.7385425 - 0)/0.50800517 = -1.4538

Here for degree of freedom = 210 - 1 = 209

and 0.05 signficance level

t_critical = 1.9714

Here l t l < t_critical so we fail to reject the null hypothesis and conclude that return in TLS stock is not different from 0%.

now for stock 2 BHP

Null Hypothesis : H₀ : = 0%

Alternative Hypothesis : H_a : 0%

Test statistic

t = (-0.399923172- 0)/0.564401885 = -0.7086

Here for degree of freedom = 210 - 1 = 209

and 0.05 signficance level

t_critical = 1.9714

Here l t l < t_critical so we fail to reject the null hypothesis and conclude that return in BHP stock is not different from 0%.

now for stock 3 CBA

Null Hypothesis : H₀ : = 0%

Alternative Hypothesis : H_a : 0%

Test statistic

t = (-0.514242394- 0)/0.507107254= -1.014

Here for degree of freedom = 210 - 1 = 209

and 0.05 signficance level

t_critical = 1.9714

Here l t l < t_critical so we fail to reject the null hypothesis and conclude that return in CBA stock is not different from 0%.