A generic brand of all-purpose fertilizer G claims to contain 10percent phosphorous, a nutrient which helps plants grow strong rootsystems. A leading name brand of all-purpose fertilizer Nadvertises having a phosphorous concentration at least 30 percenthigher than the generic brand. The most important consideration isthat the mean phosphorous concentration in each brand is at leastas high as advertised; a slightly higher phosphorous concentrationis not concerning, but having too little phosphorous will hurt orslow the growth of plants’ root systems. Further, brand N issignificantly more expensive than brand G per pound, so consumerswho purchase brand N fertilizer expect the product to producestronger root systems as advertised.
You work for a consumer protection group that has receivedcomplaints about both brands. The complainants claim that the meanphosphorous concentration in each fertilizer is lower thanadvertised. Additionally, you wish to determine whether brand N’sclaim of having a phosphorous concentration at least 30% higherthan brand N is true. If any of the companies’ claims are found tobe untrue, the consumer protection group will bring a class-actionlawsuit against the brand or brands responsible.
The consumer protection group bought bags of each brand offertilizer and sent them to a lab for analysis. The phosphorouscontent (as a percent) for each bag, along with a column indicatingwhich brand produced the bag is detailed below:
Phosphorous (% per bag), Brand
9.79522878032876, G
10.9302191178489, G
12.1732852582726, N
9.0544640624081, G
10.0475170197499, N
11.6656993826563, N
12.6642653530907, N
9.10468690374451, G
9.03436435420168, G
13.7352205503801, N
14.5489736025146, N
9.77948772403382, N
12.2986303191169, N
10.3807530975497, G
12.1950434195649, G
9.36377060086138, G
9.35399703787208, G
11.6263999062187, N
14.8368893022518, N
10.3076684543705, G
8.95153287738328, G
9.38069973700502, G
12.2352561489847, N
8.75328753808385, G
7.67158718250212, G
11.060128497079, N
13.3621542490895, N
12.1468548485131, N
9.32726632730324, N
12.2110173028274, N
9.41454096948369, G
10.4809518447645, N
9.96123587641246, G
10.1635577800051, G
10.8408606925903, N
16.1557438655007, N
7.94990087762832, N
9.44666693523413, G
9.16255880009391, G
10.8115193560222, G
a) What is the appropriate hypothesis test to determine whetherbrand G has the mean phosphorous concentration advertised?
b) What is the appropriate hypothesis test to determine whetherbrand N has the mean phosphorous concentration advertised?
c) What is the appropriate hypothesis test to determine whetherbrand N has a mean phosphorous concentration at least 30% higherthan brand G as advertised?
