Answered: s there a statistically significant…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Hypothesis Testing Question Option #2:

2. Is there a statistically significant difference between Idaho and Montana in terms of the proportion of the adult population that has been vaccinated for COVID-19? The proportion of citizens from each state that have reported being fully vaccinated is below. Results are from representative samples. Use the five step model and write a sentence or two interpreting your results (use p= .01, Z(critical) = ± 2.58).

Idaho Montana

P_s1 = .42 P_s2 = .49

N₁ = 425 N₂ = 281

Expert Solution

Step 1

Solution:

Given information:

$n_{1} = 425 S a m p l e s i z e o f I d a h o n_{2} = 281 S a m p l e s i z e o f M o n \tan a \hat{p_{1}} = 0.42 S a m p l e p r o p o r t i o n o f I d a h o \hat{p_{2}} = 0.49 S a m p l e p r o p o r t i o n o f M o n \tan a α = 0.01 L e v e l o f s i g n f i c a n c e \hat{p} = \frac{n_{1} \times \hat{p_{1}} + n_{2} \times \hat{p_{2}}}{n_{1} + n_{2}} \hat{p} = \frac{425 \times 0.42 + 281 \times 0.49}{425 + 281} \hat{p} = \frac{178.5 + 137.69}{706} \hat{p} = \frac{316.19}{706} = 0.4479 P o o l e d p r o p o r t i o n$