In 1993 a study found that 18 of lakes were contaminated wit

In 1993, a study found that 18% of lakes were contaminated with dangerous levels of sulfur. Recent samples of water from 2969 lakes showed that 606 were contaminated with dangerous levels of sulfur. At a significance of 0.05, has proportion of lakes polluted by sulfur increased?

At this level of significance, we cannot say the proportion has increased.

The proportion has increased.

Solution

The test hypothesis:

Ho: p=0.18 (i.e. null hypothesis)

Ha: p>0.18 (i.e. alternative hypothesis)

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(606/2969-0.18)/sqrt(0.18*(1-0.18)/2969)

=3.42

It is a right-tailed test.

Given a=0.05, the critical value is Z(0.05) = 1.645 (from standard normal table)

The rejection region is if Z>1.645, we reject the null hypothesis.

Since Z=3.42 is larger than 1.645, we reject the null hypothesis.

Answer: The proportion has increased.