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April 10th, 2014, 05:30 PM  #1 
Newbie Joined: Apr 2014 From: Hungary Posts: 7 Thanks: 0  I need help with this statistic question please!
A fast food restaurant reports that the mean food energy of their cheese burger is 1311kJ with a standard deviation of 100kJ. In a random sample of 5 cheese burgers it was found that the food energy content was 1290, 1443, 1421, 1390, 1475 kilojoules. (a) Find the sample mean food energy content of the burgers. I got 1403.8 for this. (b) Find the sample standard deviation. I got 63.31 for this one. (c) The public expect organisations to accurately report nutritional informa tion. Perform a hypothesis test to determine if the fast food restaurant has been honest with its published food energy data for its cheese burg ers. In doing this test be sure to (i) State the null and alternative hypotheses. I just don't know how to this question (i). like I know null hypotheses means when all the numbers are equal and alternate means they are not, but how do I do I apply this to the question. 
April 12th, 2014, 12:33 AM  #2 
Senior Member Joined: Nov 2013 From: Baku Posts: 502 Thanks: 56 Math Focus: Geometry  It is Easy
First write down sample statistics. $\displaystyle m_1 = 1311 \\ sd_1 = 100 \\ m_2 = 1403.8 \\ sd_2 = 63.31$ Assuming your calculations is correct. $\displaystyle H_0$ : Null hypothesis. $\displaystyle H_A$ : Alternative hypothesis. $\displaystyle H_0 : m_1 = m_2 \\ H_A : m_1 \neq m_2$ Now, lets calculate pvalue. (Note that it is two sided (or twotailed) test) $\displaystyle P(observed \; or \; extreme\; outcome \;  \; H_0 \; is \; true)$ $\displaystyle se = \frac{63.31}{\sqrt{5}}=28.31$ $\displaystyle \triangle z = \frac{1403.81311}{28.31} = 3.28$ Now, go to link: pvalue and enter the value and you will get pvalue = 0.001. Therefor we reject null hypothesis. Notes: 1. $\displaystyle P( x>3.28 ) = P ( x< 3.28 ) = 0.000538 $ . Because of it is two tailed we sum up each tail. (approx. 0.001) 2. The default significance level $\displaystyle ( \alpha ) $ is 0.05. If $\displaystyle pvalue < 0.05$ , we reject $\displaystyle H_0 $ 3. I just did calculations, and not shared much information. If you want to know how to do hypothesis tests, just ask. 

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