Question

3. A certain chemical pollutant is in the Hudson River. After environmental efforts the average is supposed to be ?=34 ???. We may assume that x follows a normal distribution with ?=6 ???. A random sample at 40 locations has a sample mean of 32.5 ppm. Use a 5% level of significance and test whether the mean amount of pollutant is less than 34 ppm?

a) State the null hypothesis H and the alternate hypothesis H.

b) What is the value of the sample test statistic (either z or t)?

The sample test statistic is and the value is_______

c) Find the P-value or show the critical region and critical value(s) on a graph of the sampling

distribution.

The P-value is ________

d) Based on your answers for parts (a) through (c), will you reject or fail to reject the null

hypothesis? Explain your answer.

Answer 1

(a)The Hypothesis:

H0: = 34

Ha: < 34

This is a Left Tailed Test.

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(b) The Test Statistic: Since the population standard deviation is known and n > 30, we use the z test.

The test statistic is given by the equation:

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(c) The p Value:    The p value for Z = -1.58, is; p value = 0.0571

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(d) The Decision Rule:   If P value is < (0.05), Then Reject H0.

The Decision:   Since P value (0.0571) is > (0.05) , We Fail to Reject H0.

The Conclusion: There isn't insufficient evidence at the 95% significance level to support the claim that the mean amount of pollutant is less than 34 ppm.

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