A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 25 bottles and finds the average amount of liquid held by the bottles is 11.7 ounces with a standard deviation of 0.2 ounce. Calculate the appropriate test statistic.

Step-by-step explanation:

Information given

represent the sample mean of amount of liquid

represent the standard deviation

sample size  

represent the value that we want to check

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

System of hypothesis

We want to verify if the true mean for the amount of liquid is lower than 12 ounces, and the hypothesis are given by:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

 (1)  

Replacing we got:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)