Answered: A random sample of 287 people are asked if they like eating hot dogs and 182 said they do. Comfort Food Magazine states that the proportion of people who like…

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Description: A random sample of 287 people are asked if they like eating hot dogs and 182 said they do. Comfort Food Magazine states that the proportion of people who like to eat hot dogs is 69%. Is there sufficient evidence to conclude that the proportion of peo

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Question

A random sample of 287 people are asked if they like eating hot dogs and 182 said they do. Comfort Food Magazine states that the proportion of people who like to eat hot dogs is 69%. Is there sufficient evidence to conclude that the proportion of people that like to eat hot dogs is fewer than or equal to 69% based on level of significance of 0.06?

c) To find our Critical Value(s) (CV), will we use invNorm(), invT()?
Select an answer v
d) Please explain the reason for the correct answer for step c.
Select an answer
Round to Two Decimal Places
CV =
f) What formula will we use for the test value?
р — р
Oz =
p•q
Ot =
yn
(T1 – F2) – (µ1 – µ2)
Ot =
n1
(ê1 – P2) – (pi – p2)
Oz =
1
Oz =

Expert Solution

Step 1

Suppose, p be the claimed proportion of people who like to eat hot dogs.

and $\hat{p}$ be the sample proportion of people who like to eat hot dogs.

The hypothesis of this test is

$H_{0} : the proportion of people who like to eat hot dogs is p vs H_{a} : the proportion of people who like to eat hot dogs is \leq p .$

The test statistics of this test,

$By CLT, Z = \frac{\hat{p} - p}{\sqrt{\frac{pq}{n}}} \overset{a}{\to} N (0, 1) for large n . where, n is the sample size, and q = 1 - p .$

Then the critical value of this test is $τ_{α},$ at a level of significance $α .$

The $τ_{α}$ is defined as, $P [Z > τ_{α}] = α .$

Step 2

c) To find out the critical value, invNorm( ).

d) Since, the critical value is $τ_{α}$ .

and the $τ_{α}$ is defined as, $P [Z > τ_{α}] = α .$

and Z follows Normal distribution hence, the correct choice is invNorm( ).

At a given level of significance, $α = 0.06$

$\begin{array}{rcl} τ_{α} & = & τ_{0.06} \\ = & 1.55 \end{array}$

Therefore, the critical value is 1.55.

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