Question

The human carcinogen dioxin can be produced by the burning of common trash. Trash from a random sample of 15 families that are avid recyclers contained a mean of 232.9 picograms/kg of dioxin, with a standard deviation of 39.9 picograms/kg. At a = 0.05, do these results provide evidence that the mean dioxin content of recyclers' trash is higher than the 200 picograms/kg produced by a well-run municipal incinerator? Answer this question by testing the null hypothesis H.: <200 against the alternative hypothesis H: > 200. Use a = 0.05. (a - 8 pts.) Compute the value of the test statistic. Show the formula and all computations, (6 - 8 pts.) Identify the rejection region. You may use a diagram or picture if you want. Be sure to explain how you obtain any numbers that you use. (c- 8 pts.) Draw a conclusion about dioxin in trash and express it meaningfully in words. Fully justify this conclusion (d - 10 pts. Construct a 95% confidence for mean dioxin content of recyclers' trash. Round the result to two digits past the decimal, and include appropriate units. Explain the meaning of this confidence interval in terms of dioxin in trash.

Answer 1

the test statistie X-ll sun ...t=.3.1935 t - - 232.g- 200 39.9 / UTS 6 x=0.05 in=15. 12, in-1 = 1.7613 If t-test statisticago) the we reject Ho to, nel 7613 Liny t: 3.1935 (c) Here t 7 tarzin-t .. lale rejeet Ho There is sufficient acidence to conclude that the mean dioxin content of recycler's rath is higher than 200 picograms Ilg. (d) 2-0.05 staunt = 2.1498 The 95% col form is Ixt to 232.9 € 2.19 48 x 39.9 the 95%0.1. for all is (210.80 Picogram /ica to 254.99 picograms led tue are 95% confident that the meam dioxin recyceris frash is falls with in the inter you 210.80 plcograms/leg to 254.99 p.grams

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