Question

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.

Answer 1

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