dse 2007 Q57 doubt

[bhavya jain]

how will we do this question-
Q57) in a survey of 400 likely voters,215 responded that they would vote for the ruling party  and 185 responded that they would vote for the opposition party.let p denote the fraction of all likely voters who preferred the ruling party at the time of the survey and let p* be the fraction of survey respondents who preferred the ruling party.find standard error of p*
a) 0.025
b) 0.035
c) 0.045
d) 0.055

[kangkan]

use rootover [(p(1-p)/n]

[The Villain]

@bhavya
X~Bin(n,p)
X~N(np,np(1-p))
 and therefore X/n~N(p,p(1-p)/n)

now variance is p(1-p)/n
just take rootover of var...u'll get standard error :)

[Dreyfus]

Let X be the people who preferred ruling party. Now X can vary from 0 to 400 ie its a rv which follows binomial distribution as there can be only two outcomes. Then p* = X/n where n=400. So p* is also follows binomial distribution with parameters p= 215/400 and q= 185/400 .
The standard error of p* = (Var(p*))½ = ((1/n²)*var(X))½
Var(x) = npq
Now ull get ur answer. Note that p* is estimator of true proportion of people who preferred ruling party!

[Spiti]

In q60, how to check if candidate is preferred or not in district A? I cant get what the null hypothesis is in this case.

[The Villain]

Spiti
59...Ho:μ1=μ2                
H1:μ1not equal to μ2

use diff of means statistic
the calculated value is coming out to be -2.49
so null hyp is rejected at 5% level but accepted at 1% level

[Spiti]

Yes. I got 59. I wanted 60th, 2nd part, where its said that candidate is preferred in dist A

[The Villain]

take p1>p2 as alternate hypothesis..null hyp is same as p1=p2

[Spiti]

Ok. So value of test statistic comes out to be 1.763, which is greater than 1.645( critical value for 5% one tailed test). So we accept that candidate is preferred in dist A,. Is that it?

[The Villain]

Yeah exactly!!null hyp gets rejected ...and so we can say candidate is preferred in district a

[Spiti]

Thanks man

[mrittik]

spiti how do you get this value? plz help

[Spiti]

Use this formula

Q=1-P

[shar311]

Hey spiti, can you please state the null hypothesis for the first part of q60

[Sris]

hey yar this is a 2014 coversation of our seniors...no one wud reply...

anyways coming to ur question...

a) null hypothesis=>>>  p1=p2
 alternate hypothesis+>>>p1 not equal to p2
use a two tail test...apply the formula that is given in the image