<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>
</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>
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</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>