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A random sample of 38 wheel chair users were asked whether they preferred cushion type A or B, and 28 of them preferred type A whereas only 10 of them preferred type B. Use a hypothesis test to assess whether it is fair to conclude that cushion type A is at least twice as popular as cushion type B.

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Answer:

The statement that cushion A is twice as popular as cushion B cannot be verified

Explanation:

From the question we are told that:

Sample size n=38

Type a size A
X_a=28

Type a size B
X_b=10

Generally the probability of choosing cushion A P(a) is mathematically given by


P(a)=(28)/(38)


P(a)=0.73

Generally the equation for A to be twice as popular as B is mathematically given by


P(b)+2P(b)=3P

Therefore Hypothesis


Null H_0: p \leq (2P)/(3P) \\Altenative H_A:p>(2P)/(3P)

Generally the equation normal approx of p value is mathematically given by


z=(x-np_0-0.5)/(√(np_0(1-p_0)) )


z=(28-(38*2/3)_0-0.5)/(√(38*2/3*1/3) )


z=0.75

Therefore from distribution table


Pvalue=1-\theta (0.75)


Pvalue=0.227

Therefore there is no sufficient evidence to disagree with the Null hypothesis
H_0

Therefore the statement that cushion A is twice as popular as cushion B cannot be verified

User Wili
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