<p>Hi, all.</p>
<p>I'm stuck on a problem in Statistics concerning Confidence Intervals and Hypothesis Testing. I was wondering if anybody could help me out.</p>
<p>A poll of voters in a neighborhood find that 540 of n=1000 contacted "support Obama"</p>
<p>a) Let p represent the proportion of all Neighborhood voters who support Obama. Find a point estimate for p.
Solved: 0.54 (540/1000) or 54% support Obama.</p>
<p>b) State the one-tailed hypothesis for predicting at (a=.05) his victory. Explain on the numbers if you should reject that hypothesis. GIVE CI AND P-VALUE</p>
<p>I got the confidence interval @ 95% of [0.514,1] since it is one-tailed from the normal distribution.....I don't know how to connect it to hypothesis testing.</p>
<p>Is the null hypothesis [0.514, 1] or 0.5 or what?</p>
<p>Thanks for anything that can help me. Thanks!</p>
<p>If the proportion you stated in your null hypothesis is in your confidence interval, then you cannot reject the null hypothesis. You are 95% certain/confident that the proportion will lie from one point to the other, and because your proposed null proportion lies in that interval you cannot say at an alpha-level of 0.05 that it it can't be that proportion :S</p>
<p>Make sure that you state it within the context of the problem (the AP test is HUGE on that) and that you state the whole 95% confident thing. Also, make sure that your analysis doesn't say "well the proportion MUST be true then"--null hypothesis testing is just trying to prove something incorrect, as you will never know true population parameters unless you take a really well-designed census (which is extremely costly and uncommon; samples usually work much better even if we are always uncertain).</p>
<p>Also... I'm pretty sure the confidence interval should be [0.509, 0.571]. Your confidence interval looks way too large for a sample size of 1000 :S</p>
<p>(sorry for the repetition... I dunno what's going on with my post)</p>
<p>Don't know if you still need this but I'm pretty sure this is the correct answer (it's been awhile and it's late at night):</p>
<p>
[quote]
State the one-tailed hypothesis for predicting at (a=.05) his victory.
[/quote]
</p>
<p>H0: P=.5
Ha: P>.5</p>
<p>(I'm using .5 as his "victory", but it's a pretty vague question. Obviously a candidate can win with lower percentages and .5 is technically a tie.)</p>
<p>
[quote]
confidence interval @ 95% of [0.514,1] since it is one-tailed from the normal distribution
[/quote]
</p>
<p>Confidence intervals are always +/- an equal amount (margin of error) from the .54. tan2007 found the correct CI. One-tailed means NOTHING for CIs.</p>
<p>Going back to the 1-side hypothesis test, we would calculate this:</p>
<p>z= (.54-.5)/(sqrt((.5(1-.5))/1000) </p>
<p>which would get us our z allowing you to find p. (Remember: One-sided, ie don't double it.) And accept/reject null based on your z and a a=.05 (z=1.645). Because your CI is only above .5 I would say that we are 95% confident that Obama would be victorious IN THAT NEIGHBORHOOD. </p>
<p>Concl. of Hyp. test: If the true prop of voters for obama is .5, we have a P chance of getting.... Because p is less than .05 we reject in favor of the null, where p>.5.</p>
<p>Remember, because the sample was taken from a single neighborhood it can only be generalized back to that neighborhood.</p>
<p>I'm lazy and took a LOT of shortcuts there but that's the gist of it.</p>
<p>Someone should check this for correctness. Like I said, it's been awhile.</p>