Minimum average of data sets?

[somename]

So we were given some excel chart on chocolate boxes, each containing 10 chocolate bars.
The data shows us the date of production for each box and also the individual weight of each chocolate bar inside said box.
(The dataset is huge, thats why each student was only given 1 production date to focus on)

The production date i got assigned to contains 2 boxes:
The individual weight of the ten bars of box A ranges from 18,07 grams to 18,82 grams. (Calculated average: 18,57 grams)
The individual weight of the ten bars of box B ranges from 18,02 grams to 18,94 grams. (Calculated average: 18,317 grams)


The question is as follows:
On basis of the given data to box A, can one evidentially say that the average weight of all chocolate bars produced on the same day turns out to be at least 18,02 grams? The significance level shall be 5.71%

I literally dont understand that question. I know its probably about hypothesis testing, but i have no starting point.

 

[Romsek]

i) you are going to model individual chocolate bar weights and thus the average of these as a normal random variable.

ii) we model each chocolate bar by the mean weight, and a standard deviation, [MATH]\sigma_p[/MATH], such that the range of observed values is with 6-10 standard deviations. Usually 6 is fine and is the most conservative estimate.

iii) given that population model, the sample model has the same mean but with [MATH]\sigma_s = \dfrac{\sigma_p}{\sqrt{n}}[/MATH]Here [MATH]n=10[/MATH]
iv) so now you have a distribution of the average. You should be easily determine the probability that the average is less than 18.02g.
Is that probability less than 5.71%? If so you can say based on the evidence to the given significance that the average is > 18.02g.

 

[somename]

Thank you Romsek for leading me on the right path.
I think my hypothesis testing should be right.

I've got:

[MATH]\bar{x} = 18.57[/MATH], [MATH]\sigma = 0.02 [/MATH], [MATH]n = 10 [/MATH][MATH]\mu_{0} = 18.02[/MATH][MATH]\alpha = 5.71% [/MATH]

[MATH]H_{0}[/MATH]: [MATH]\mu < 18.02 [/MATH][MATH]H_{1}[/MATH]: [MATH]\mu\geq 18.02 [/MATH]
z-value: [MATH] \frac{\bar{x} - \mu_{0}}{\frac{\sigma}{\sqrt{n}} } = 0.8696 [/MATH]
critical value of [MATH]z_{1} - \alpha = 1,579[/MATH]
Since z-value [MATH]<[/MATH] critical value, do not reject [MATH]H_{0}[/MATH].

So this means that - with the level of significance being 5.71% - there is not enough evidence to prove that the average weight of chocolate bars is greater than 18,02. Right?

 

[Romsek]

First off the z-value is, in your notation,

[MATH]\dfrac{\mu_0 - \bar{x}}{\frac{\sigma}{\sqrt{n}}} =\cdot \dfrac{18.02 - 18.57}{\sigma_s} = [/MATH]
Next. I get

[MATH]\sigma_p = \dfrac{18.82 - 18.07}{6} = 0.125[/MATH]
[MATH]\sigma_s = {\sigma_p}{\sqrt{10}} \approx 0.04[/MATH]
[MATH]z = \dfrac{-0.55}{0.04} \approx -13.75[/MATH]
[MATH]\text{The z-score of 5.71% is about -1.58}[/MATH]
H1 resoundingly wins

 

[somename]

Ok i did some research and appearently you're right. My numerator should've been

[MATH]-\bar{x}+\mu_{o}[/MATH]
But im really asking myself why that is the case.

Edit: Ohhh is it because i switched around my hypotheses?