Question

A philanthropic organization helped a town in Africa dig several wells to gain access to clean water. Before the wells were in place, an average of 120 infants contracted typhoid each month. After the wells were installed, the philanthropic organization surveyed for four months and found an average of 90 infants contracted typhoid per month. Assume that the population standard deviation is 40 and the number of infants that contract typhoid is normally distributed. Calculate the value of the appropriate test statistic.

Answer 1

Answer: -1.5

Step-by-step explanation:

When population standard deviation is known, then the formula to find the z-test statistic for population mean is given by :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

, where n= Sample size.

$\mu$ = Population mean

$\overline{x}$ = Sample mean

$\sigma$= Population standard deviation.

As per  given , we have $\mu=120$ (average infants contracted typhoid each month)

$\sigma=40$

n= 4 (No. of months)

$\overline{x}=90$

Then , the value of the appropriate test statistic will be :

$z=\dfrac{90-120}{\dfrac{40}{\sqrt{4}}}$

$z=\dfrac{-30}{\dfrac{40}{2}}$

$z=\dfrac{-30}{20}$

$z=-1.5$

Hence, the value of the test statistic = -1.5