Hypothesis testing | Mathematics homework help

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Attached is a multiple choice worksheet on hypothesis testing

 

PROBLEM 1

In India, both average clearing time and the variance of clearing times are large (“clearing time”

is time for funds to be transferred when a payment is authorized). You are a consultant who

has been hired by India to improve efficiency of the banking system by reducing both the

average and the variance. You install new hardware and software, and reorganize work flows.

Before your reforms, mean clearing time between any pair of large or medium-sized cities was

3.9 days, and the population standard deviation of check-clearing times was 1.5 days. (These

values were known.)

Now you want to demonstrate the impact of your reforms on average clearing time. You take a

random sample of 41 clearing times since your reforms were implemented. In this sample, the

mean clearing time is 3.5 days, and the sample standard deviation of clearing times is 1.1 days.

A normal plot indicates that clearing times are approximately normally distributed.

CQ1. Which are the appropriate null and alternative hypotheses?