In 1965, about 44% of the U.S. adult population had never smoked cigarettes. A national health survey of 1205 U.S. adults (presumably selected randomly) during 2006 revealed that 615 had never smoked cigarettes.
Reference: Ref 18-5
Suppose you wished to test whether there has been a change since 1965 in the proportion of U.S. adults that have never smoked cigarettes. Which of the following are the appropriate hypotheses?
A. H0: p = 0.44, Ha: p > 0.44
B. H0: p = 0.51, Ha: p 0.51
C. H0: p = 0.44, Ha: p 0.44
D. H0: = 0.44, Ha: 0.44
The P-value of the test of hypotheses is
A. greater than 0.10.
B. between 0.05 and 0.10.
C. between .01 and 0.05.
D. below 0.01.

- KonradZuse

- katieb

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- KonradZuse

@jim_thompson5910

- jim_thompson5910

what did you get for the first part

- KonradZuse

I forgot to mention that there was a misprint when I pasted.. B is not equal, same with C, and then there is a p ^ for both of D's answers... I think it's B....

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## More answers

- jim_thompson5910

D is out because you're not testing p^, you're testing p

- jim_thompson5910

how are you getting 51% ?
the given percentage is 44%

- jim_thompson5910

oh i see, you divided 615/1205 = 0.51, but that's p^ and NOT p

- KonradZuse

I meant C?

- jim_thompson5910

you did eh? lol
yeah C is correct

- KonradZuse

Haha I glanced over them didn't realize that there were 2 of the same haha... I wanted the one that was not equal :D.

- KonradZuse

Would the next part be B?

- jim_thompson5910

you first need to find the test statistic

- KonradZuse

hmm....

- jim_thompson5910

use the formula
z = (m - p)/(sqrt(pq/n))
where m is the test statistic and q = 1-p
z = (m - p)/(sqrt(pq/n))
z = (0.51037 - 0.44)/(sqrt(0.44*0.56/1205))
z = 4.92108
So the test statistic is z = 4.92108

- jim_thompson5910

now you need to find P(z > 4.92108) and double this result

- jim_thompson5910

you can get away without even using a calculator though because notice how far z = 4.92108 is from z = 0

- KonradZuse

mhm,.

- jim_thompson5910

so what's the p value

- KonradZuse

not b hmm? A?

- jim_thompson5910

what did you get for the p-value, which numeric value did you get

- KonradZuse

not sure....

- jim_thompson5910

calculate P(z > 4.92108), what do you get

- KonradZuse

How do we calculate that again without the table?

- jim_thompson5910

type
normalcdf(4.92108, 10)
into wolfram alpha

- jim_thompson5910

or you can use a TI calculator to do the same thing

- KonradZuse

hm.... Now the le end poin is almos 5, but the oher bnumbers are super tiny

- jim_thompson5910

so that means what

- KonradZuse

A or D.

- jim_thompson5910

why A

- KonradZuse

Well like I said I wasn't sre if it was the 5 or tiny #'s.. So D then :)

- jim_thompson5910

well the p value is very very small, so it has to be less than 0.01

- jim_thompson5910

the p value is the 4th value down

- jim_thompson5910

well you double it first, but still, it's very small

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