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April 10th, 2014, 05:30 PM   #1
OMg
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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.
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April 12th, 2014, 12:33 AM   #2
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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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