Question

1. The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer. The levels, in ppm, are shown below.

0.31 0.47 0.19 0.72 0.56

0.91 0.29 0.83 0.49 0.28

0.31 0.46 0.25 0.34 0.17

0.58 0.19 0.26 0.47 0.81

Do the data provide sufficient evidence to support the claim that the mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0.4 ppm? Use a 0.05 significance level to test the claim that these sample levels come from a population with a mean greater than 0.4 ppm. Use the P-value method of testing hypotheses. The population standard deviation is unknown.

options are:

a) P-value: p = 0.0435 Because p < alpha, we reject the null hypothesis. There is sufficient evidence to support the claim that u>0.4ppm

b) P-value: p = 0.8035 Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that u>0.4ppm

c) P-value: p = 0.1965 Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that u>0.4ppm

d) P-value: p = 0.3929 Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that u>0.4ppm

Answer 1

Null Hypothesis H0: Mean level of the chemical in tomatoes from this producer is equal to the recommended level of 0.4 ppm. That is = 0.4 ppm.

Alternative Hypothesis H0: Mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0.4 ppm. That is > 0.4 ppm.

From the data,

Sample mean = 0.4445

Sample Standard deviation, s = 0.2276765

Standard error of mean = s / = 0.2276765 / = 0.0509

Since we do not know the population standard deviation, we use one-samples t test.

Test statistic t = ( - ) / Std Error = (0.4445 - 0.4) / 0.0509 =  0.8743

Degree of freedom = n-1 = 20 - 1 = 19

P-value = P(t > 0.8743) = 0.1965

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0.4 ppm.

c) P-value: p = 0.1965 Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that u>0.4ppm