Question

The Environmental Protection Agency recommends that concentrations of the carcinogenic insecticide mirex found in salmon, be at a level of no more then 0.08 parts per million. Researchers tested 75 randomly chosen farm-raised salmon for 45 different farms and found the mean concentration of mirex to be 0.0853 with a standard deviation of 0.0315. A histogram of the distribution was fairly symmetric and showed no outliers. Are farmed salmon contaminated beyond the level permitted by the EPA? Use a significance level of � = 0.01.

a) State the hypotheses in symbols. (2 points)

b) Use your calculator to perform a 1-Sample t-Test and report the test statistic and p-value. Do not make these calculations by hand. Instead, use the T-Test command in your graphing calculator found under STAT – TESTS. Write out what you entered in your calculator. (3 points)

c) Make a sketch of the test distribution. Be sure to label the test statistic and p-value. Your graphing calculator will make this sketch for you if your choose “Draw” instead of “Calculate” in the test input screen. (2 points)

d) Write a full conclusion for this test in the context of the problem (See previous assignment for format). (4 points)

e) Find a 98% confidence interval for the mean concentration of mirex found in farm-raised salmon. Do not make these calculations by hand. Instead, use the TInterval command in your graphing calculator found under STAT – TESTS. Write out what you entered in your calculator. (3 points)

f)Interpret the confidence interval in the context of this problem. (2 points)

g) Does this confidence interval support your conclusion in part (d)? Explain. (2 points)

Answer 1

a) H₀: < 0.08

    H₁: > 0.08

b) The test statistic t = ()/(s/)

                                 = (0.0853 - 0.08)/(0.0315/)

                                 = 1.457

P-value = P(T > 1.457)

             = 1 - P(T < 1.457)

             = 1 - 0.9253

             = 0.0747

c)

d) Since the P-value is greater than the significance level (0.0747 > 0.01), so we should not reject the null hypothesis.

So there is sufficient evidence to conclude that farmed salmon contaminated beyond the level permitted by the EPA.

e) At 98% confidence interval the critical value is t^* = 2.378

The 98% confidence interval is

+/- t^* * s/

= 0.0853 +/- 2.378 * 0.0315/

= 0.0853 +/- 0.0086

= 0.0767, 0.0939

f) We are 98% confident that the true population mean concentration of mirex found in farm-raised salmon lies in the above interval.

g) Since the confidence interval cointains only positive values, so it support the conclusion in part(d).