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a.The null hypothesis is stated as follows:

$H_0:{蟽}^2=100$(The population of institutional investors does not perform consistently).

The alternate hypothesis is stated as follows:

$H_a:{蟽}^2<100$(The population of institutional investors performs consistently).

b. Using $伪=0.05$and $(n-1)=199$, ${蠂}^2$value of rejection is found in table IV of Appendix D. However, since we have to determine the lower tail value, which has$伪=0.05$ to its left, we used the ${蠂}_{0.95}^2$column in table IV.

Therefore the rejection region is given by ${蠂}^2<167.361$.

c. The value of $伪$means that the chance of concluding that the alternative hypothesis is true when actually the null hypothesis is true is 0.05.

In the words of the problem it means, chance of concluding $蟽<10$that when actually $蟽=10$is 0.05.

d. From the Minitab printout we find,

The test statistic is ${蠂}^2=154.71$ and the $p-value=0.009$.

e. Since the test statistic gives us a value of${蠂}^2=154.71$ which does not fall in the rejection region, therefore we will reject the null hypothesis$H_0:{蟽}^2=100$ which says the population of institutional investors does not perform consistently.

Therefore, the alternative hypothesis $H_a:{蟽}^2<100$which specifies that the population of institutional investors perform consistently is accepted.

The assumption required is that the rates of return must follow a normal distribution for the inference to be valid.