Question

1. Question 3 part 1: A researcher wants to know whether Aurors (magical police) have different drink preferences than the general wizarding population (these are known from prior research). He takes a sample of n = 300) Aurors and asks each one what their favorite drink is (see the table below). The goal was to see whether Aurors’ preferences differed from those of the general population. Assume all assumptions are met. Do all hypothesis testing for this part of question 3 using α = 0.01. (See table below for sample data.)

Favorite Drink

                                                 Pumpkin juice       Butterbeer       Firewhisky       Elven Wine

81	131	59	29
46 %	41 %	11 %	2 %

Observed Valuesn =300

Expected Proportions

Answer the questions labeled "Question 3 part 1" in the Word document using this information.

Question 3 part 2: A researcher wants to know whether there is any relationship between a person’s preferred type of magic (light, neutral, or dark) and the type of animal they chose as their familiar (owl, cat, or rat). To investigate this, she takes a sample of n =250) people and records how many people fall into each of the categories. The goal of the study is to test whether there was any relationship between the two variables. Assume all assumptions are met. Do all hypothesis testing for this part of question 3 using α =0.05. (See table below for sample data.)

Observed Frequencies

Preferred Animal Familiar

                                                                                     Owl      Cat                 Rat

57	20	41
19	23	18
31	22	19

Light magic118

Type of magic preferred                                            Neutral magic60

Dark magic72

Answer 1

if we have given the observed frequencies and expected frequencies and also categorical variables the best test statistic willbe Chi Square test

3(1) Here we need to test the goodness of fit means how far is the observed frequency fit to the population or expected frequency

We will for the null hypotheis Ho: There is no significant differnece between the Aurors and the normal population.

H1: There is a sgnificant differnce between the Aurors and the normal population

The test statistic will be used as Chi square where =

The calculation will be done in the below table

Oi is the given observed frequency and Ei we need to calculate from the % given multiplied by 300 willl give each Ei

From that we have the value of   = 132.72 and the degree of freedom for a Chi square will be (c-1) (r-1) where r is the row and c is the column.

We have 4 columns and 1 row so we can take is as 4-1 = 3 df= 3

From the p value calculator for p= .00001 at significant level of

so if we have a p vlaue which is lower than the significance level we eed to reject the null hypothesis.

Here the null hypothesis says that there is no difference between the Aurors and the normal population in prefence of drinks if we rejct this we need to accpet the null hypothesis that there is a differenc in the preference of Aurors .

3(2) This is a problem of Test of independence using Chi square

The null hypothesis will be Ho : There is no relation between the the person's preferred type of magic and their familiar animal they choose

So the Alternate hypothesis becomes H1: There is some relation between the persons preferred type of magic anf the amilar animal they choose

The test statistic will be used as Chi square where =

The calculation will be done in the below table

Here we have given a sample size of 250

But not given the Ei or any values

So we find Ei using the formaul = row total x column total /Grand total for each item if we take first row first column cell we take firs column total x first row total / grand total here grand total is 250

WE have the value of = 11.41 degree of fredom = 3-1x3-1= 2x2=4 the significance level given is = 0.05

So the p value will be p = 0.0223 < 0.05 so here also we rejct the null hypothesis of there is no relation between the two criteria and accept the hypothesis that there is some relation

Hence we can conlclude that there is some relation between the preferred magic type and the familiar animal they choose