# Answer in Statistics and Probability for chris #230932

The mass of a standard loaf of white bread is, by law meant to be 700g with a population standard deviation of 21g. The Lauren Bakery, which supplies outlets throughout the Eastern Cape, regularly checks the masses of its standard loaf of bread white bread. If their bread is underweight, on average, they are liable for a fine by the Provincial Department of Health, whose inspectors undertake random checks. If the bread is overweight, on average, the bakery is wasting its ingredients. On a given day, a random sample of 64 loaves is selected and weighed. The sample mean mass was found to be 695g. Assume that the mass of bread is approximately normally distributed 3.2 Polokwane Butchery supplies Vienna sausages in the entire of KZN province. An Inspector from the CCSA has been sceptical of the mass of the Vienna sausage packs after receiving numerous complaints. He wants to investigate the marked mass shown on Vienna sausages. A pilot study showed a mean of 11.8kg per pack and a variance of 0.49kg

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Answer in Statistics and Probability for chris #230932
Just from $13/Page Given the information: For a standard loaf of white bread, Hypothesized mean “\mu_o=700” Population standard deviation “\sigma=21” Sample size “n=64” Sample mean “\overline{x}=695” We have given, mass of bread is approximately normally distributed. Here we assume the level of significance “\alpha=0.05” Here to check if breads are overweight or not. We use z test statistic Hypothesis to test “H_o:\mu=700” “H_1:\mu>700” Region rejection: “Z_c=Z_\alpha=Critical” “Value” Where “\alpha=0.05” “Z_c” is the critical value from Z – table at “\alpha=0.05” Therefore, “Z_c=Z_\alpha=1.645” Critical rejection region “R=\left\{Z:Z>1.645\right\}” Test statistic: “z=\frac{\overline{x}-\mu }{\frac{\sigma }{\sqrt{n}}}=\frac{695-700}{\frac{21}{\sqrt{64}}}=-1.905” Decision rule: “z=-1.905<Z_c=1.645” Hence we accept “H_o” at “\alpha=0.05” and we can conclude that there is no overweight production of bread. Now, from “z-table” we find out “p-value” for “z=-1.905” “p-value=p(z>-1.905)” “=0.9716” If “p-value>level” “of” “significance(\alpha)” “p-value=0.9716>\alpha=0.05” Hence, we accept “H_o” at “\alpha=0.05” Conclusion We can conclude that there is no overweight production of bread. 3.2 Given: Sample mean “(\overline{x})=11.8” Sample variation “(s)^2=0.49” Sample standard deviation “(s)=\sqrt{s^2}” “=\sqrt{0.49}” “s=0.7” Margin error “=0.2” Confidence level(CI) “=99”% We have to find out how many packs should the inspector sample out In short we have to find out sample size. We know that, “Confidence\:Interval=\overline{x}\:\pm margin\:of\:error” “=\overline{x}\:\pm Z\alpha \left(\frac{s}{\sqrt{n}}\right)” Here we have given margin of error Margin of error “=Z\alpha \times(\frac{s}{\sqrt{n}})” “0.2=Z\alpha \times \left(\frac{0.7}{\sqrt{n}}\right)” Where, “Z\alpha” is a critical value derived from “z-statistical” “table” For confidence level “=99”% “(1-\alpha)=0.99” “\alpha=0.01” “Z\alpha=0.01=2.576” “0.2=2.576\times \left(\frac{0.7}{\sqrt{n}}\right)” “n=\left(\frac{2.576\times 0.7}{0.2}\right)^2” “n=80.72\approx 81” Therefore, we can say that 81 samples are required to find out 99% confidence that sample mean will differ by 0.2g. # What Will You Get? We provide professional writing services to help you score straight A’s by submitting custom written assignments that mirror your guidelines. #### Premium Quality Get result-oriented writing and never worry about grades anymore. We follow the highest quality standards to make sure that you get perfect assignments. #### Experienced Writers Our writers have experience in dealing with papers of every educational level. You can surely rely on the expertise of our qualified professionals. #### On-Time Delivery Your deadline is our threshold for success and we take it very seriously. We make sure you receive your papers before your predefined time. #### 24/7 Customer Support Someone from our customer support team is always here to respond to your questions. So, hit us up if you have got any ambiguity or concern. #### Complete Confidentiality Sit back and relax while we help you out with writing your papers. We have an ultimate policy for keeping your personal and order-related details a secret. #### Authentic Sources We assure you that your document will be thoroughly checked for plagiarism and grammatical errors as we use highly authentic and licit sources. #### Moneyback Guarantee Still reluctant about placing an order? Our 100% Moneyback Guarantee backs you up on rare occasions where you aren’t satisfied with the writing. #### Order Tracking You don’t have to wait for an update for hours; you can track the progress of your order any time you want. We share the status after each step. #### Areas of Expertise Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types. # Trusted Partner of 9650+ Students for Writing From brainstorming your paper's outline to perfecting its grammar, we perform every step carefully to make your paper worthy of A grade. ##### Preferred Writer Hire your preferred writer anytime. Simply specify if you want your preferred expert to write your paper and we’ll make that happen. ##### Grammar Check Report Get an elaborate and authentic grammar check report with your work to have the grammar goodness sealed in your document. ##### One Page Summary You can purchase this feature if you want our writers to sum up your paper in the form of a concise and well-articulated summary. ##### Plagiarism Report You don’t have to worry about plagiarism anymore. Get a plagiarism report to certify the uniqueness of your work. ## Free Features$66FREE

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