Soup Dumplings

At each restaurant, Chris randomly sampled $8$ dumplings and measured the following about each dumpling:

Restaurant : $($string$)$ the restaurant's name

Soup: $($float$)$ the amount of soup, in grams

Meat : $($float$)$ the amount of meat, in grams

Skin : $($float$)$ the thickness of the dumpling skin, in millimeters

Type : $($string$)$ the type of meat used in the dumpling

Location : $($string$)$ the neighborhood where the restaurant is located

They put this data into a dumpling table. Here are the first four rows:

$\backslash$table$[[$Restaurant$,$Skin,Meat,Soup,Type,Location$],[$Jiadia JangBao,$1\mathrm{.}15,8\mathrm{.}60,5\mathrm{.}78,$Pork,Puxi$],[$NaxXiang ManTou Dian,$1\mathrm{.}40,11\mathrm{.}68,5\mathrm{.}02,$Crab,Puxi$],[$Paradise Dynasty,$1\mathrm{.}12,12\mathrm{.}65,4\mathrm{.}83,$Pork,Pudong$],[$Din Tai Fung,$1\mathrm{.}04,9\mathrm{.}39,5\mathrm{.}02,$Shrimp,Pudong$]]$

$(412$ rows omitted$)$

Chris also created a Soup Dumpling Index to objectively measure the quality of a soup dumpling. Here is the formula:

Soup Dumpling Index $=\frac{\text{M}\text{e}\text{a}\text{t}\text{W}\text{e}\text{i}\text{g}\text{h}\text{t}+\text{S}\text{o}\text{u}\text{p}\text{W}\text{e}\text{i}\text{g}\text{h}\text{t}}{\text{S}\text{k}\text{i}\text{n}\text{T}\text{h}\text{i}\text{c}\text{k}\text{n}\text{e}\text{s}\text{s}}$

Question $1\mathrm{.}1.(1$ pts$)$ Select the null hypothesis that Ming should use to assess her claims.

On average, dumplings made in Puxi have a higher Soup Dumpling Index by $2\mathrm{.}1$ than dumplings from Pudong.

Dumplings made in Puxi have the same Soup Dumpling Index distribution as those made in Pudong.

On average, dumplings made in Puxi have a higher Soup Dumpling Index than those made in Pudong, due to chance.

On average, dumplings made in Puxi have a higher Soup Dumpling Index than those made in Pudong.

Dumplings made in Puxi have a different Soup Dumpling Index distribution than those made in Pudong.

$3$

Question $1\mathrm{.}2.(1$ pts$)$ Select the alternative hypothesis that Ming should use to assess her claims.

On average, dumplings made in Puxi have a higher Soup Dumpling Index by $2\mathrm{.}1$ than dumplings from Pudong.

Dumplings made in Puxi have the same Soup Dumpling Index distribution as those made in Pudong.

On average, dumplings made in Puxi have a higher Soup Dumpling Index than those made in Pudong, due to chance.

On average, dumplings made in Puxi have a higher Soup Dumpling Index than those made in Pudong.

Dumplings made in Puxi have a different Soup Dumpling Index distribution than those made in Pudong, due to chance.