My Math Forum I need help with this statistic question please!

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 April 10th, 2014, 04:30 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 11th, 2014, 11:33 PM #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 p-value. (Note that it is two sided (or two-tailed) test) $\displaystyle P(observed \; or \; extreme\; outcome \; | \; H_0 \; is \; true)$ $\displaystyle se = \frac{63.31}{\sqrt{5}}=28.31$ $\displaystyle \triangle z = \frac{1403.8-1311}{28.31} = 3.28$ Now, go to link: p-value and enter the value and you will get p-value = 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 $\displaystyle p-value < 0.05$ , 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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