Hippocrates magazine states that 33 percent of all Americans take multiple vitam

Question

Hippocrates magazine states that 33 percent of all Americans take multiple vitamins regularly. Suppose a researcher surveyed 750 people to test this claim and found that 274 did regularly take a multiple vitamin. Is this sufficient evidence to conclude that the actual percentage is different from 33% at the 5% significance level?
Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].  

a) [p-value = 0.090, FRH0]

b) [p-value = 0.040, FRH0]

c) [p-value = 0.020, FRH0]

d) [p-value = 0.040, RH0]

e) [p-value = 0.020, RH0]

Explanation / Answer

Sol:

Ho:p=33%=0.33

Ha:p 0.33

alpha=0.05

test statitsic:

p^=sample pro=x/n=274/750=0.365333

z=p^-p/sqrt(p(1-p)/n)

=0.365333-0.33/sqrt(0.33(1-0.33)/750

=2.06

p value=0.0394

p=0.04

p<0.05

Reject Ho

ANSWER:

d) [p-value = 0.040, RH0]

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