Question

Hippocrates magazine states that 35 percent of all Americans take multiple vitamins regularly. Suppose a researcher surveyed 750 people to test this claim and found that 296 did regularly take a multiple vitamin. Is this sufficient evidence to conclude that the actual percentage is different from 35% at the 5% significance level?

Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [p-value = 0.060, FRH0]

b) [p-value = 0.010, FRH0]

c) [p-value = 0.010, RH0]

d) [p-value = 0.005, RH0]

e) [p-value = 0.005, FRH0

Answer 1

p value = 0.005 for right tailed

Reject H0

Explanation:

Given that Hippocrates magazine states that 35 percent of all Americans take multiple vitamins regularly.

Persons surveyed = 750

Of those survived no of persons who took multiple vitamin = 296

Sample proportion = p =0.395

q =1-p = 0.605

`H_0:  p=0.35\\H_a:  p\\eq 0.35`

(Two tailed test)

Assuming H0 is true standard error =
`√(0.35*0.65/750) \\=0.0174`

p difference = 0.045

Test statistic =
`(0.045)/(0.0174) \\=2.58`

p value = 0.005 for right tailed

Reject H0

Option d is right