and 2 for 50 months each. The mean and the standard deviations of the monthly returns of Funds 1 and 2 are as follows: Fund 1: ?̅1 = 6.5761, ?1 = 6.1737, Fund 2: ?̅2 = 3.7232, ?2 = 6.5833. Can we conclude at the 5% significance level that the mean of the monthly returns (in %) of Fund 1 ex
(a) A group of researchers randomly sampled and recorded the monthly returns (in %) of Funds
1 and 2 for 50 months each. The mean and the standard deviations of the monthly returns
of Funds 1 and 2 are as follows:
Fund 1: ?̅1 = 6.5761, ?1 = 6.1737,
Fund 2: ?̅2 = 3.7232, ?2 = 6.5833.
Can we conclude at the 5% significance level that the mean of the monthly returns (in %)
of Fund 1 exceeds that of Fund 2? Assume that the two populations of monthly returns
are
(b) In addition to Funds 1 and 2 in (a), the same group of researchers randomly sampled and
recorded the monthly returns (in %) of Funds 3 and 4 for 50 months each. The mean and
the standard deviations of the monthly returns of Funds 3 and 4 are as follows:
Fund 3: ?̅3 = 4.7852, ?3 = 6.0538,
Fund 4: ?̅4 = 7.0224, ?4 = 6.2643.
Can we conclude at the 5% significance level that there are differences among the means
of the monthly returns (in %) of Funds 1-4? Assume that the four populations of monthly
returns are normally distributed and that these populations have equal variances.
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