Question

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/m3 and a standard deviation of 3.92 g/m3 . 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) Define the parameter of interest using the correct notation. Then, state the null and alternative hypotheses for this study.

(b) Calculate the observed value of the test statistic. State the distribution (and degrees of freedom if needed) it follows.

(c) Compute the p-value or provide a range of appropriate values for the p-value.

(d) Using the significance level α = 0.025, state your conclusions about if the chemical plant is in violation of the working code

Answer 1

PATE Sample <30 16.98 g/m3 Soluhon(a) Here Size M17 Hente the sample Also sample na The. Population on stendard deviakon Students is small sampe mean u= 15.08 m² 3 SD = 3.923) t-text We at use stepl Null hypothers to the chemical plant is in violation of the working code Step 2 Alternative hypothely Hi. The choices plant is in not riolation of the Working Code step3 Level of significance significance o=0-025 Stepy by calculation of the test statistic tz n- u 16.98- 15.0 B 3.92 x= 16.98 uz15 n=17 17-) Sa 3.92 16.98-15.0 -1.98 E-8.02 E 098 It=2.02 , the Calutate t F value 9.02 slim 392

(©) The t tabulate rake of t al 2.50% Level of significan and 16 degree of freedom Y Q.120 o 025 (d) since calulate value of t > rake of t at a=0.0 16 degree of freedos therefore HO y rejected ; the chemical Chemical plant is in no of the work violation code sking tabulate & with Du