Question

9. A chemical plant is required to maintain ambient sulfur dioxide concentration levels in the working environment atmosphere at an average level of no more than 15.0 g/m3. The results of 17 randomly timed measurements of the sulfur dioxide level produced a mean of 16.98 g/m² and a standard deviation of 3.92 g/m? Test if the chemical plant is in violation of the working code. If needed, assume that the ambient sulfur dioxide concentration level is normally distributed. (a) [2 marks] Define the parameter of interest using the correct notation. Then, state the null and alternative hypotheses for this study. (b) [1 mark] Calculate the observed value of the test statistic. State the distribution (and degrees of freedom if needed) it follows. (c) [1 mark] Compute the p-value or provide a range of appropriate values for the p-value. (d) [1 mark] Using the significance level a = 0.025, state your conclusions about if the chemical plant is in violation of the working code.

Answer 1

Here we have: X = 16.98 S= 3.92 n = 17 a = 0.025 Hypothesis: Hou < 15 Hai u >15 Test statistics: t-distribution (o unknown) χ-μ t = 16.98-15 3.92 = 2.08 S Vn V17

df = n-1 = 17-1 = 16 w P-value = p (t>12.081) = 0.02698 Fail to reject the null hypothesis. Conclusion: Here we have sufficient evidence to reject the null hypothesis. P- value is greater than alpha value. We can support the claim that the working environment atmosphere at an average level of no more than 15.0 g/m3