3. Does the label \"GLUTEN FREE\" guarantee that a food has absolutely NO gluten

Question

3. Does the label "GLUTEN FREE" guarantee that a food has absolutely NO gluten? The New York Times on 5/20/2015 published an article titled "Study Finds that Probiotics Labelled Gluten Free Often Aren't". It reported that FDA guidelines state a product must contain less than 20 parts per million of gluten to qualify as gluten free. They reported that some products exceed that but claim to be gluten free, but also noted that some products containing gluten may legally qualify as gluten free. Dr. P.H.R. Green of the Celiac Disease Center, Coumbia University, was quoted that some people "may be much more sensitive to even less than 20 parts per million". Suppose that a product claiming to be gluten free was tested and that in a sample of 7 batches of this product the gluten levels in parts per million were: 15 9 20 14 22 14 12 Perform a hypothesis test to determine if the average gluten content is less than 20 parts per million so that the manufacturer can support its claim that the product can be represented as gluten free. Perform a hypothesis test to determine if the average gluten content is less than 20 parts per million so that the manufacturer can support its claim that the product can be represented as gluten free. Use a 3% level of significance.

Explanation / Answer

H0: =20

Ha: 20

Calculate t- statistic

t =( x(bar) – )*sqrt(7)/SE(x)

xbar = 15.143 , SE(x) = 17.26

t =( 20-15.143)*7 / 17.26

t = 1.97 ,

t- critical at =0.03, df = 6

t-critical = 2.82. Since the t-critical is greater than t- calculated , so we do not reject the null hypothesis.

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