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  = 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_o:  < 200 against the alternative hypothesis H₁:  > 200. Use  = 0.05.

(A- 10 points)Compute the value of the test statistic. Show the formula and all computations.

(b – 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

we are 95 % confident that the true mean dioxin content of recyclers’ trash lies between 210.804 and 254.996