Question

13) You are an environmentalist interested in the prevalence of acid rain (as measured by the pH of the rainwater) in the northeaster United States. Assume that the mean "normal" pH for pure rain falling through clean air is about 5.7. You randomly collect and test 39 samples of rainwater in the northeastern United States and calculate a sample mean pH of 5.5 with a known population standard deviation of 6. Explain why the initial requirements have been met and whether to use the tor z table. Using this data, test the claim that northeastern rainfall is more acidic than it should be, that is, that the mean pH is lower than the "normal" value of 5.7? Test using a = .05.

Answer 1

Since sample size is 39 so using CLT we can assume that sampling distribution will be normally distributed.

Since population standard deviation is known so z test can be used.

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Here we have I =5.5,0 =6, n =39 Hypotheses are: H:> 5.7 H :/< 5.7 Level of significance: a =0.05 Test is one tailed (left tailed). Test Statistics: -- I-u = (5.5-5.7)/(6/sqrt(39)) 0 = -0.21 Critical value: Rejection Region: -1.645 If z<-1.645, Reject HO Decision: Since test statistics dose not lie in rejection region so we fail to reject the null hypothesis P-value: P-value=0.4168 Decision: Since p-value is not less than level of significance so we fail to reject the null hypothesis Excel function for critical value: Excel function for p-value ENORMSINV(0.05) =NORMSDIST(-0.21)

Conclusion: There is no evidence to conclude that mean PH is lower than normal value 5.7.