Use the following for next 2 questions. As a safety recommendation to recreation

Question

Use the following for next 2 questions. As a safety recommendation to recreational shers,the EPA recommended screening value for Mirex is 0.08ppm. Fish with higher values are not safe for human consumption. Researchers tested three farm-raised salmon for organic contaminants. They found the mean concentration of the carcinogenic insecticide Mirex to be 0.16 parts per million, with standard deviation 0.06 ppm. Does the sample give evidence that farm-raised sh do not meet EPA guidelines?

36. The hypotheses of interest are

(A) H0 : µ = 0.08 vs. Ha : µ < 0.08

(C) H0 : µ = 0.16 vs. Ha : µ < 0.16

(B) H0 : µ = 0.08 vs. Ha : µ > 0.08

(D) H0 : µ = 0.16 vs. Ha : µ > 0.16

(E) H0 : ¯ x = 0.08 vs. Ha : ¯x > 0.08

37. A one-sample t-test was computed and the Pvalue was found to be 0.07. Although the results .
(A) are statistically signicant at = 0.05, the explanation is that the sample size is small and it isn’t surprising to nd the results to be statistically signicant.

(B) are statistically signicant because the mean is equal to 0.16, they are not of practical importance. (C) are statistically signicant at = 0.05, the explanation is that P-value was computed incorrectly.

(D) are not statistically signicant at = 0.05, the explanation is that the sample size is small and it isn’t surprising to nd the results to be not statistically signicant. (E) are not of practical signicance they are statistically signicant at = 0.05.

Explanation / Answer

36. The hypotheses of interest are

(A) H0 : µ = 0.08 vs. Ha : µ < 0.08 INCORRECT

(C) H0 : µ = 0.16 vs. Ha : µ < 0.16 INCORRECT

(B) H0 : µ = 0.08 vs. Ha : µ > 0.08   CORRECT

(D) H0 : µ = 0.16 vs. Ha : µ > 0.16 INCORRECT

(E) H0 : ¯ x = 0.08 vs. Ha : ¯x > 0.08   INCORRECT

Obviously Null hypothesis will be when we assume that mean concentration of the carcinogenic insecticide Mirex is equal to 0.08 ppm so only option (A) and (B) are correct.and we have to find out that in sample if there is more concentration of Mirex so it becomes right side one directional test. so option A is left directional so it can be eliminated so Option C is right.

Q.37 As we have performed one sample t - test and P - value was found equals to 0.07

t = (0.16 - 0.08)/ (0.06/sqrtn)

P - value = 0.07 so t value is less than 1.65 so that means sample size can be said pretty small in the range of 4 or 5 only.

so this p- value is greater than significance level alpha equals to 0.05 so the null hypothesis cannot be rejected so we can say the results are not statistically signicant at = 0.05, the explanation is that the sample size is small and it isn’t surprising to nd the results to be not statistically signicant.

so option D is correct.

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