Question

Suppose you wish to determine if there has been a change in water quality since the City
opened up a new water treatment facility at the end of 2018. You test water at entry, from
52 homes in the area, in two separate years: 2018, and 2019.

SEdiff =0.036, x-bar 2018=0.87, x-bar 2019=0.94, n=52, boxplot shows a very small left skew.

Perform a hypothesis test at the 2.5% level of signficance (recall this means that the
likelihood of us falsely rejecting H0 is only 2.5/%.). You will need to find a Z-score,
and see if it lands inside the “rejection region” or not.

Answer 1

Hypotheses are:

The z-score is

It is given that

so,

Test is two tailed so critical values for 2.5% level of significance using exel functions "=NORMSINV(0.0125)" and "=NORMSINV(1-0.0125)" are -2.241 and 2.241.

The rejection region is

If z <= -2.241 and z >= 2.241, reject H0

Since z does not lie in the rejection region so we fail to reject the null hypothesis.