refer to image Cadmium, a heavy metal, is toxic to animals. (The chemical abbreviation for Cadmium is Cd.) Mush-rooms, however, are able to absorb and accumulate cadmium at high concentrations. The Czech andSlovak governments have set a safety limit for cadmium in dry vegetables at 0.5 part per million (ppm).M. Melgar et. al. measured the cadmium levels in a random sample of the edible mushroom Boletuspinicola and published the results in "Influence of Some Factors in Toxicity and Accumulation of Cdfrom Edible Wild Macrofungi in NW Spain (Journal of Environmental Science and Health, Vol. B33(4),pp. 439-455). The data obtained by the researchers are below. Past data suggest that that Cd in thepopulation of Boletus pinicola to be normally distributed. Researchers want to test whether the meanCadmium levels in this population of mushrooms exceeds the safety limit.0.24 0.59 0.62 0.16 0.77 1.33 0.92 0.19 0.33 0.25 0.59 0.32(a) Find the sample mean (include units), sample standard deviation, sample size, and write down theadditional information given in this problem with correct notation. Round the sample mean to fourdecimal places(b) The researchers would like to test the hypothesis at the 10% level. Determine which hypothesistesting method applies and check it satisfies all 3 conditions.(c) Identify the null and alternative hypotheses using statistical notation & in words.

Given data: X 0.24 0.59 0.62 0.16 0.77 1.33 0.92 0.19 0.33 0.25 0.59 0.32 Where X denotes Cadmium levels.a) The table below shows the necessary calculations: Sample x x-x2 1 0.24 0.0817 2 0.59 0.0041 3 0.62 0.0089 4 0.16 0.1338 5 0.77 0.0596 6 1.33 0.6467 7 0.92 0.1554 8 0.19 0.1128 9 0.33 0.0383 10 0.25 0.0761 11 0.59 0.0041 12 0.32 0.0424 SUM 6.31 1.3639 Average 0.5258 The sample size is n=12. The sample mean is obtained below: x¯=∑xn=6.3112≈0.5258 ppm The sample standard deviation is obtained below: s=∑x-x¯2n-1=1.363912-1≈0.3521 The additional information is that the population mean is μ=0.5.b) The t-test procedure will be applicable here. Reason: To test the single population mean, there are only two methods, the t-test and the z-test. As the population standard deviation is not given, the t-test procedure will be used. Assumption: It satisfies all the conditions as it is given that the data comes from a normal population, the population standard deviation is unknown, and the sample is a random sample.c) The null and alternative hypotheses are respectively stated below: H0: μ=0.5 (The mean Cadmium level is 0.5 ppm) Vs H0: μ>0.5 (The mean Cadmium level exceeds 0.5 ppm)