Hypothesis Testing

For this assignment, we want to test a hypothesis:

Based on

statista.com, $12\mathrm{.}8$ percent of Canadians are left$-$handed.

The Countries With The Most

Left$-$Handed People

Rate of left$-$handedness in selected countries

We want to test this number and see if this proportion is the same in Concordia. Use

the $8$ step process to test this hypothesis. Your population is all current students.

STEP $1$: $[5$ marks$]$

STEP $2$: $[5$marks$]$

STEP $3$: Use alpha of $0\mathrm{.}05.$

STEP $4$: $[5$ marks$]$

STEP $5$: Gather Data

a$.$ What should be the sample size? $($Assuming an acceptable Error of $0\mathrm{.}12)$

$[10$ marks$]$

b$.$ How do you select your sample and how do you gather data? For this step

you need to actually collect data. You should ask students whether they

are left$-$handed and record data. $[7$ marks$]$

c$.$ Create a table here and present your sample. Create a table the size of

your sample, and in each cell write L for students who are left$-$handed, and

$R$ for students who are right$-$handed. $[10$ marks$]$

For example, if your sample size is $12$:

STEP $6$: $[12$ marks$]$

a$.$ In addition to the test statistics $[6$ marks$],$ find the p$-$value $[6$ marks$]$ of the

sample as well.

STEP $7$: $[8$ marks$]$

STEP $8$: $[5$ marks$]$

No matter what your statistical conclusion is$,$ you might be committing an Error:

a$.$ What is the probability of committing Type I Error? $[5$marks$]$

b$.$ What is the probability of committing Type II Error: $[$for each part draw the

graph and show the region of interest$)$

i$.$ If alternative proportion is the same as US proportion? $[7$marks$]$

ii$.$ If alternative proportion is the same as Netherlands proportion?

$[7$marks$]$

iii. If alternative proportion is the same as India proportion? $[7$marks$]$

iv$.$ If alternative proportion is the same as China proportion? $[7$marks$]$