4) Two investment managers are being considered by an investor who needs someone
ID: 3313521 • Letter: 4
Question
4) Two investment managers are being considered by an investor who needs someone to look after her money. Manager B would be preferable, because his costs are less, but only if it clearly does not result in a reduced mean return on her investment. To test, the investor gives each manager 8 portfolio's to manage and records their investment return on each. The sample mean return for manager A was 5.7% with sample standard deviation 0.8%, while for manager B the sample mean return was 5.5% with sample standard deviation 0.6%. a) Should the investor not switch over to manager B? Test at a significance level of 5%. b) What is the (approx imate) p-value for the test?Explanation / Answer
Solution:-
a)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: A> B
Alternative hypothesis: A < B
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.3536
DF = 14
t = [ (x1 - x2) - d ] / SE
t = 0.57
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 0.56. We use the t Distribution Calculator to find P(t < 0.57) = 0.71
Therefore, the P-value in this analysis is 0.71
Interpret results. Since the P-value (0.71) is greater than the significance level (0.05), we cannot reject the null hypothesis.
Since we do not have suffcient evidence that mean return is not reduced for Manager B. Hence we should not invest in manager B.
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