(8 pts) A coin is tossed 10,000 times, and it lands heads 5,167 times. Is the chance of heads equal to 50 percent? Or are there too many heads for that? We can formulate this in terms of a test of significance. Tossing the coin is like drawing at random with replacement 10,000 times from a 0-1 box, with 0 = tails and 1 = heads. The fraction of 1's in the box is unknown. Null hypothesis: this fraction equals 1/2. Alternative: the fraction is bigger than 1/2. The number of heads is like the sum of the draws.

The SE for the sum of 10000 draws is(. )

Compute the z-test statistic for the observed number of heads.(correct to 2 decimal places)===

Find the observed significance level or P-value of the statistic. Write your answer as a decimal correct to four decimal places..

Note: Since P is so small, we reject the null hypothesis that the observed large number of heads is due to chance.