Question

1. In a random sample of 32 large cap mutual funds, the average YTD return is 3.05% with a standard deviation of 9.77%. Conduct by hand an appropriate hypothesis test at the 5% level to test whether the average YTD return for a large cap mutual fund is positive. (Again, that means to write the hypotheses, compute the test statistic, and estimate the p-value.) Give your test conclusion in terms of the question being asked. Confirm your test statistic and result with Minitab. Also, interpret the associated confidence bound for this test.

Answer 1

Given: n=32, X=3005 Sz9077 Hypotheses & но сре 0 Hi & M 70 Sürce sample standard deviation only known , We will use t-statistic. Test statistic: X-M ~ tn-l 3.05-0.2 9.77/132 107659.

e Value - 0004363 (from Praline for) funlue u lip Alon А1о-о) therefore there is supcient evidence to reject Ho. Hence there is enough evidence to conclude that average YTD rerun for a large cap neutual fund is positive condedevee 'suesval 3- X tertical value S + critical value at tzo.os, df = 81 z 196960 z | 3.05(1696) x ( 40 777 - (06/2082, 509797) Tues means that 95% CI calculated will not tam actual 132 population mean in between them.

From Minitab it can be done in the following steps:

Choose Stat > Basic Statistics > 1-Sample t