Question

A company that produces food supplements is under investigation by trading standards for making false claims. The company produces protein bars, stating on the package of its product that they contain 20 grams of whey proteins and 10 grams of proteins from a vegetable source, cheaper than whey proteins. This is thought not to be true after a number of complaints were filed against the company by retailers. It is in fact believed that the true mean whey protein content in the bars produced by the company is less. A sample of 25 packs of protein bars were analyzed. The sample gave an average whey protein content of g 18.9 and standard deviation s = 1. Construct and interpret a 95% confidence interval for the mean whey protein content 2. Should trading standards take action against the company? Perform a statistical test to decide, taking a 0.05 and calculating the p-value. Is the test conclusive? Discuss. 3. What error could you have made in making your decision in (2)? Explain 4. A larger sample of 90 packs of protein bars has been analyzed for further investigations, giving this time an average whey protein content of g same hypothesis of point (2). Is the result in line with the previous conclusion? 19.2 and standard deviation s = 4.3. Test the

Answer 1

we have i na sample size=25 . ng a sample mean = 18.9 "= population mean = 20 . 4 s= 3.1 claim :- It is fact believed that the true mean. produced whey the bass protein content in company is less. by the 0 95% confidence interval for the mean whiley protein content. MECT: † (t12,df * Fon)] here of an-t=24 tale, df = to.osizi = + 2.064 from table)

= [ 18.9 + 12.064 * 3.1 =[ 18.9 € 1.2796] = (17.620, 20.1796] that population mean we can say 95%. confident 17.620 4 20.179.. an " whey protein is lies within Ø Perform statistical test - To test : Ho: M=20 vs H,: MC20

Test statistic i t= = Ý :-) sis. (18.9-20) 525 3:1 T= 7.7741) Test statistic is -1-4741 = Itl= 1-1-7741 = 1-7741 Now critical value = tala, df = 1711 1 Decision :- we reject Ho at (1-2) H100 % level of here Illa tolla,df significance hence we if IH> talline of reject Ho.

conclusion :- There is enough evidence to conclude that the frue mean whey protein content in the bars produced by the company is less. *) P value = 0.0447 - cfoom Tables using p value approach we reject Ho if pralue ca value hore p value <a ralue hence we reject Ho. at a= sy. * . prading standards should not take action against the company. © we can use or got Type I essor here we reject Ho at a=57

| 0 0- 49, 9= 11, 2, 5 = 42. .. test the same hupothesis of point ® * To test i Ho: 4= 20 vs Hi M220 ne sam Test statistic it = ray-u)In - (19.2-20) 590 : 4:3 TE= 4.7649) here df = n-1=89. ta121 of = toos, 89 7.662/ p value = 0.040922 ) - (from table)

Decision in we reject Ho at (1-2)X100 ). level of significance if it > td12.0f $ P valve cd value & p value <a value hese IH > thia, df hence we reject Ho.. conclusion - that the true the bars there is enough mean whey produced by the evidence protein company to conclude content in is lers.