Statistics - Homework Solution | California State University, Northridge

University:
California State University, Northridge
Course:
MATH 340 | Introduction to Probability and Statistics
Academic year:

2009
Views:

148

Pages:

1
Author:

Leticia Watts

3. Industrial pollution often makes water supplies acidic (pH < 7) or basic (pH >7). An industrial company claims that the mean pH level of the water in a nearby river is 7, so it is neutral. You, as an environmentalist, randomly select 19 water samples and measure the pH of each. The sample mean and standard deviation are 6.9 and 0.24, respectively. Assume the population of pH levels in all possible water samples is normally distributed. a. Is there enough evidence to reject the company’s claim at the 5% significance level? At the 10% level? Step 1: state the hypothesis: H0 : µ = 7 Ha : µ ≠ 7 Step 2: Conditions: random sample (checked), the population is normally distributed, so that’s checked too. Step 3: find the sample statistics: x = 6.9 Step 4: find the test statistic: t = x − µ0 6.9 − 7 = = −182 . s 0.24 n 19 Using the calculator: STATTESTS2:T-Test Step 5: p-value = 0.086 Conclusion: At the 5% level: Since the p-value is greater than 5%, we cannot reject the null hypothesis. That is, we don’t have enough evidence to reject the claim that the mean pH level is 7. At the 10% level: Since the p-value is less than 10%, we can reject the null hypothesis. That is, we have enough evidence to reject the claim that the mean pH level is 7. b. Can you reach the same conclusion using the appropriate confidence interval for the mean pH level? Yes, we can use a confidence interval to test the claim because we have a two-tailed test. (≠ in the alternative hypothesis) The 95% confidence interval is (using 8:TInterval): (6.7843, 7.0157). Since 7 is inside the interval, then at the 5% level we cannot reject the null hypothesis. Same conclusion as above. The 90% confidence interval is (using 8:TInterval): (6.8045,6.9955). Since 7 is outside the interval, then at the 10% level we can reject the null hypothesis. Same conclusion as above.