Problem 5: Mercury in Freshwater Fish (20 points) Experts believe that 20% of al
ID: 3153582 • Letter: P
Question
Problem 5: Mercury in Freshwater Fish (20 points) Experts believe that 20% of all freshwater fish in the United States have such a high level of mercury that they are dangerous to eat. Suppose a fish market has 250 fish tested and 60 of them have dangerous levels of mercury. Test the hypothesis that this sample is not from a population with 20% dangerous fish. Use = 0.10.
i. State the null and alternative hypotheses.
ii. State the significance level for this problem.
iii. List the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic.
iv. Calculate the p-value and include the probability notation statement.
v. State whether you reject or do not reject the null hypothesis. vi. State your conclusion in context of the problem (i.e. interpret your results).
vii. Use StatCrunch to verify your test statistic and p-value.
Explanation / Answer
i.
Formulating the null and alternatuve hypotheses,
Ho: p = 0.2
Ha: p =/= 0.2 [ANSWER]
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ii.
As given,
alpha = 0.10 [ANSWER]
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iii.
As the n = 250, p = 0.20, then np and n(1-p) are both greater than 10, so we can use the normal approximation.
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iv.
As we see, the hypothesized po = 0.2
Getting the point estimate of p, p^,
p^ = x / n = 0.24
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.025298221
Getting the z statistic,
z = (p^ - po)/sp = 1.58113883
As this is a 2 tailed test, then, getting the p value,
p = 0.113846298 [ANSWER, P VALUE]
Hence, if the null hypothesis is true, the probability of getting a sample at least as extreme as out result is 0.1138. [ANSWER]
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v.
As P > 0.10, we FAIL TO REJECT THE NULL HYPOTHESIS.
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vi.
There is no significant evidence at 0.10 level that this sample is not from a population with 20% dangerous fish. [CONCLUSION]
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