Need help with p-value question
"According to an exit poll in the 2006 Virginia senatorial election, 50.1% of the sample size 2011 reported voting for James Webb. Is this enough evidence to predict who won? Test that the population proportion who voted for Webb was 0.50 against the alternative that it differed from 0.50. Answer by
b) Stating hypotheses and checking assumptions for a large-sample test.
c) Reporting the P-value and interpreting it. (The test statistic equals 0.09.)"
Am I correct in stating that the null hypothesis is H0: p=.5 and HA: p does not equal .5 (i.e., the little not equal symbol)? If so, do I want to use a two-tailed test?
Second, using the z=(p-hat - p=.5)/se_null (which is sqrt of .5(.5)/2011), I did find that the z-score rounds to .09, which, according to my z-table, gives a p-value of .5359. First, are the z-table figures analogous to p-values, and second, and am I supposed to subtract .5359 from 1 to get the tail value, and then multiply that by 2? I've gone over the text repeatedly but can't seem to figure it out.
Third, if anybody knows the TI-83, I'm getting a different answer for the z-score by using 1-PropZTest (p0=.5, x=1005-1008 (I've tried them all, and none of them bring up .09) and n=2011). 1-PropZTest is option 5 under Stat/Tests.
If anybody can give me any guidance at all, I would appreciate it greatly.