Sugar Substitute Packet Project (Version 1) In the same week, I was talking with

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Sugar Substitute Packet Project (Version 1) In the same week, I was talking with my husband, Dr. Michael Hibbs, and a fellow teacher, Judith Peterson, and they both complained that the off-brand sugar substitute packets were not consistently measured. They are both coffee drinkers and said that sometimes when they open the package and pour it into their coffee cup, it seems like there is not as much in one packet as there is in others. This project is to test the Great Value company brand by Walmart's claim that the packets are not consistent The company's claim on the box is that there are 200 packets and that the net weight is 200 g Assume the standard deviation of the paper packet is 0.1 g and that the weight of the packets are normaly distributed. Test the company's claim using 20 packets of sugar substitute using recorded values in the provided table. On one page, give me the original claim, the remaining claim, the Hb and Hu Bive the test you are running, the values you use, draw the bell curve and label, and give the conclusion. You are then to write a letter to the company telling them what your conclusions are and make any recommendations as to their production of sugar substitute packets you feel they may or may not need to add describe your sample size, the mean of your sample and its standard deviation You should also include a statement of a 95% confidence interval in regards to their stated mean. You need to describe the variability of their product with respect to the standard deviation. This should be ress. Be sure to quantify your recommendations. This means part of your letter should written as a business letter (if you do not know how to write one, look it up! This one gives you the idea of what to do only two or three paragraphs. ). Your letter need be After my husband and fellow co-worker had made their declaration of irritation with the consistency of the sugar packets, I started paying attention to the ones I used when I made my coffee. picked a packet at random out of the box and noticed it felt light. I brought it home and weighed it. The packet, including the paper, weighed 0.6 g. Ialso found out that the standard deviation for the population is o.1. Find the probability of choosing an individual packet less than this weight. For a sample of 20 packets, find the probability that those packets have a mean weight less than 0.6g. You will need to show your work for this on a separate page. Please list your known values, show any calculations you make, draw and label the bell curve, and any other pertinent information. What would you conclude based on your results? For this project, on the parts you type,use Times New Roman, 12 font You will turn this project in to me in the following order a. Cover sheet with the title of this project, your name, the version of your project and what group and the date centered in the middle of the page. This is you are in, este double spaced fiII collea Your page with all your work for the sample. Your business letter. Adhere to the spacing format of a business letter. Be sure to sign your letter! b. c. d. Your page with all your work for the individual packet.

Explanation / Answer

Assuming you have below hypthesis and the data in your project.

H0: Null Hypothesis: Mean weight of packets is 1.0 g

H1: Alternative Hypothesis: Mean weight of packets is less than 1.0 g

In sample of 20 packets, you have measured the mean weight equal to 0.6 g. Given the standard deviation of the population is 0.1

So, the standard error of the mean = 0.1 / sqrt(20) = 0.0224

Test Statistic, Z = (0.6 - 1) / 0.0224 = -17.857

P-value P(Z < -17.857) = 0

As, p-value is less than the significance level (0.05), we reject the null hypothesis.

Conclusion: There is sufficient evidence, at the = 0.05 level (95% confidence level), to conclude that the mean weight of packets is less than 1.0 g.

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