Answer:
The statement that cushion A is twice as popular as cushion B cannot be verified
Step-by-step explanation:
From the question we are told that:
Sample size n=38
Type a size A [tex]X_a=28[/tex]
Type a size B [tex]X_b=10[/tex]
Generally the probability of choosing cushion A P(a) is mathematically given by
[tex]P(a)=\frac{28}{38}[/tex]
[tex]P(a)=0.73[/tex]
Generally the equation for A to be twice as popular as B is mathematically given by
[tex]P(b)+2P(b)=3P[/tex]
Therefore Hypothesis
[tex]Null H_0: p \leq \frac{2P}{3P} \\Altenative H_A:p>\frac{2P}{3P}[/tex]
Generally the equation normal approx of p value is mathematically given by
[tex]z=\frac{x-np_0-0.5}{\sqrt{np_0(1-p_0)} }[/tex]
[tex]z=\frac{28-(38*2/3)_0-0.5}{\sqrt{38*2/3*1/3} }[/tex]
[tex]z=0.75[/tex]
Therefore from distribution table
[tex]Pvalue=1-\theta (0.75)[/tex]
[tex]Pvalue=0.227[/tex]
Therefore there is no sufficient evidence to disagree with the Null hypothesis [tex]H_0[/tex]
Therefore the statement that cushion A is twice as popular as cushion B cannot be verified
