Question

32. A biometric system is designed to reduce the time it takes for payments to reach payees. Researchers would like to evaluate the effectiveness of using this payment system by carrying out a hypothesis test. In a certain village in India, they knew that it took on average 1.22 days for the recipients to obtain the welfare payments prior to introduction of the system.

After the system was introduced, researchers took a random sample of 46 villagers and found that it took on average 1.15 days to receive the payments, with a standard deviation of 0.21 days.

Suppose μμ is defined as the average time for villagers in the given village to receive their welfare payments using the biometric system. The researchers test a hypothesis of H0:μ=1.22H0:μ=1.22 against an appropriately selected alternative.

What distribution will be used to determine the P-value for this hypothesis test?

Select one:

a. A standard normal distribution.

b. A standard normal distribution with mean 1.22 and standard deviation 0.21.

c. A t distribution with 45 degrees of freedom.

d. A t distribution with 46 degrees of freedom.

Answer 1

Here, sample standard deviation is given with sample size 46
so, we need to use t test with degree of freedom = n - 1 = 46 - 1 = 45

So, our answer is

c. A t distribution with 45 degrees of freedom.