A consumer agency that proposes that lawyers' rates are too high wanted to estimate the

mean hourly rate for all lawyers in Kuala Lumpur. A sample of $100$ lawyers taken from Kuala

Lumpur showed that the mean hourly rate charged by them is RM$1,420.$ The population

standard deviation of hourly charges for all lawyers in Kuala Lumpur is RM$510.$

a$.$ Construct a $99\%$ confidence interval for the mean hourly charges for all lawyers in Kuala

Lumpur.

$(3$ Marks$)$

b$.$ Suppose the confidence interval obtained in part $($a$)$ is too wide, how can the width of this

interval be reduced?

$(2$ Marks$)$

$[$Total: $5$ Marks$]$

A researcher estimates that the average revenue of the largest businesses in country $x$ is

greater than RM$24$ billion. A random sample of $50$ companies is selected, and the mean

revenues is RM$28$ billion and the population standard deviation is RM$15$ billion. Test the

researcher's claim using $=0\mathrm{.}05,$ that the average revenue of the largest businesses in

country $x$ is greater than RM$24$ billion. Answer the following questions.

a$.$ Identify the claim and state the $H_0$ and $H_1.$

b$.$ Find the critical value.

c$.$ Calculate the test statistic.

d$.$ Make a decision to reject or fail to reject the $H_0.$

e$.$ Interpret the decision in the context of the original claim.