How do you find the P value of a hypothesis test?

- anonymous

How do you find the P value of a hypothesis test?

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- amistre64

its the area of the tails ....

- amistre64

determine the z or t score using the Ha as the cutoff stat for Ho
the P-value is just the area left in the tails

- anonymous

This is my particular problem: A survey of 1910 people who took trips revealed that 136 of them included a visit to a theme park. Based on those survery results, a management consultant claims that less than 8% of trips include a theme park visit. Test this claim using the alpha= .01 significance level.
Assuming Ho, The z score is?
The critical z score for declaring significance is?
The P Value of the Hypothesis test is_____?

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## More answers

- amistre64

are you using a ti83, stat program, or just tables in the book?

- amistre64

|dw:1370969246279:dw|

- anonymous

I found the z score to be -1.4168...then the critical z score using norm.s.inv(.99) on excel to be 2.32...but I do nt know how to find the p value...would I need to find the z score for .08 and use that value into norm.s.dist(z value, cumulative)? that is what I think to do...but I don't know how to find the z value with P (x<.08)

- anonymous

we have been using excel..wow I am so glad I found this site, I have been searching for a free help site and had no luck

- amistre64

1910*.08 = 153
use 153 is your test value

- amistre64

since there is no standard deviation given, should we do a t stat, or a z stat? sample size seems well over 30 to me

- anonymous

what is a t stat?

- anonymous

I believe so...you mean z score?

- amistre64

its similar to a zscore stat, but uses a t distribution as opposed to a normal distribution .... its used for unknown standard deviations

- dumbcow

@ViennaJade , Excel gives pvalue of .078 for z-score of -1.4168
"NORMSDIST(-1.4168)"

- anonymous

hmmm dumbcow let me try that

- anonymous

admiter I found the standard deviation by hand

- amistre64

136/1910 = .0712 as a "mean" this is less then 8% of the sample size already so i don think the score of 8% will be negative

- anonymous

I just checked dumbcow's answer and it was right

- anonymous

now I'm not sure I remember why his answer is right though...

- amistre64

\[\Large\frac{136}{1910}\pm Z_{.01}\left( \frac{\frac{136}{1910}\frac{1774}{1910}}{\sqrt{1910}} \right)\].01 in one tail is .02 in both tails,relates to a confidence interval of 98%, z=2.33
a confidence interval of 98% is
\[\Large .0712\pm 2.33\frac{(.0712)(.9288)}{\sqrt{1910}}\]
cows answer was correct, thats nice :)

- amistre64

opps, forgot to sqrt the whole thing

- anonymous

why are you finding the confidence interval? I'm confused

- amistre64

so an interval of .057 to infinity ....
just trying to recall some stuff.
how would you determine the test statistic for less then 8%?

- anonymous

I would want to use the z score formula , plug in 153/1910-.08 all over the standrd dev of .006208

- anonymous

and then use excel =norm.s.dist(the z score)

- amistre64

.08 - 153/1910 of course the only differnce is a sign

- anonymous

amistre thank you so much for helping me...and dumbow...do you get paid for this?

- dumbcow

http://en.wikipedia.org/wiki/Statistical_hypothesis_testing#Common_test_statistics
this problem is a 1-proportion z test right?
\[z = \frac{.08 - \frac{136}{1910}}{\sqrt{\frac{136}{1910}(1-\frac{136}{1910})}}\sqrt{1910}\]

- anonymous

dumbcow I have no idea what that equation is...we were taught that z score of p hat= p hat-Ho/stdev

- dumbcow

how are you finding std dev?

- dumbcow

sqrt{n*p*(1-p)}

- anonymous

I don't think it's 1-proportion because they want less than .08

- anonymous

stdev of p hat= sqrt(p*q/n)

- anonymous

p is .08, q is .92

- anonymous

n is 1910

- dumbcow

oh ok, well in that case you already did everything and didn't need any help :)

- anonymous

I still didn't get how you used the z score I found and used that to find the p(x<.08)? sorry..

- dumbcow

|dw:1370971511146:dw|
the p-value is the probability of being "left" of z-score on the bell curve
the excel function "normSDist" will tell you the area "left" of a given z-score

- dumbcow

if p-value < .01 , reject H0
otherwise Fail to reject H0

- anonymous

I think I get it. Thank you so much Amistre and dumbcow! :))

- dumbcow

yw

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