Question

Probe of level 8. (10 points) 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 0.35 0.46 0.25 0.34 0.17 0.58 0.19 0.26 0.47 0.81 The normal probability plot of the data is provided. At the 10% significance level, do the data provide sufficient evidence to conclude that the mean level of the chemical in tomatoes from this producer is greater than the recommended level of 0.4 ppm? a) Check assumptions and choose an appropriate test procedure. b) State the null and alternative hypotheses symbolically. c) Use 1-var-stats to find the sample mean and the sample standard deviation. d) Compute the value of the test statistic. e) Determine the P-value. Please show your work. +) Decide on the null hypothesis (reject H, or do not reject H.). ) Interpret the results of the hypothesis test. .

Answer 1

Solution We should we t - Test to do this question because n<30 t = X-u un 1=20 (size) &= Standard deviation H. = I=8-4 (all hypothelis) Hon>0.4 (altruoti bypothu.es The values are = 0-31,047,0,19,072,056,0-41,0-29,0-83, 0.49,028,0.350.46, 0.25, 0.34,0.17,0.50,- 0-19, 0.26, 0.47,081 = 0.4465 & =0 226606 t = X-un I --0-4465-0.4 20 0.226606 X =

=0917691 At boi significance level and 0-2 vellue = 1.325 .. We will accept the full hypothesis Ans = At the lol significance level the mean level ir tomatoes is not greater than 0.4 ppm of the chemical THANKS

When the sample is less than 30 we solve the sum by t distribution and when the sample is greater than 30 we do the normal distribution. s is the standard deviation. Xbar is the mean. We do not reject the null hypothesis because the value of t is less than the value at10% significance level with n=20 in the t-distribution table.

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