Question

1. Some experts believe that 16% of all freshwater fish in a country have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 200 fish tested, and 35 of them have dangerous levels of mercury. Test the hypothesis that this sample is not from a population with 16% dangerous fish, assuming the sample is random. Use a significance level of 0.05.
   1. State the null and alternative hypotheses.
   2. Determine the z-test statistic.
   3. Find the p-value
   4. Do you reject or do not reject the null hypothesis?
   5. What can you conclude?

Answer 1

a)

H0: p = 0.16

Ha: p 0.16

b)

Sample proportion = 35 / 200 = 0.175

Test statistics

z = - p / sqrt( p( 1 -p ) /n)

= 0.175 - 0.16 / sqrt( 0.16 * 0.84 / 200)

= 0.58

c)

p-value = 2 * P( Z > z)

= 2 * P( Z > 0.58)

= 2 * 0.281

= 0.5620

d)

Since p-value > 0.05 level, we do not have sufficient evidence to reject H0

e)

We conclude at 0.05 level that we fail to support the claim.