John inherited $500,000 from his grandfather two years ago, which was invested t

Question

John inherited $500,000 from his grandfather two years ago, which was invested to 30 ETF funds and 40 REITs. The mean increase for the ETF funds is $1000, with a standard deviation of $40. The mean increase for the REITs is $970, with a standard deviation of $55. Assume that the population standard deviations are equal.

(a) At the 0.05 significance level, use hypothesis testing to decide if there is a difference in the mean yields of the two funds? State the five steps of hypothesis testing clearly. (6 marks)

(b) If you are hired to give some investment suggestions to John, what analysis you plan to do and what recommendations you can make based on your potential results, in 150 words or less (4 marks)

Explanation / Answer

(aa) Here Hypothesises are

Step 1 :

Null Hypothesis : H0 : 1 = 2

Alterntive Hypothesis : Ha : 1 2

Here 1 represents ETF funds and 2 represensts REITs

Step 2 : Significance level = 0.05

Step 3 : Critical test statistic

dF = 30 + 40 - 2= 68

alpha = 0.05

tcritical = 1.9955

Step 4 : Test statistics

Here pooled standard deviation

sp = sqrt [(n1 - 1)s12 + (n2 -1)s22}/ (n1 + n2 - 2)] = sqrt [{(30 - 1) * 40 * 40 + (40 -1) * 55 * 55 }/(30 + 40 -2)]

= 49.169

standard error of difference sed= sp * sqrt [1/n1 + 1/n2] = 49.169 * sqrt [1/30 + 1/40] = 11.875

Tesst statistic

t = (x1 - x2)/sed = (1000 - 970)/11.875 = 2.526

Step 5 : The conclusion

Here as

t > tcritical   

we shall reject the null hypothesis and can claim that there is difference in the mean yields of the two funds.

(b) Now, as we know that there is significant difference in mean yields of his investment. So, as we can see that he earned most from ETF funds so he should raise his stakes in ETF funds. In parellal, he must have to reduce the number of ETFs and REITs as 30 and 40s are large amount of funds to invest. This could be better for diversification but not for getting higher return. He may continue using REITs by keeping the view of volatility in market as there may be fluctuating returns rom ETFs as compared to REITs. He may have tried other investment option to sustain his returns.

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