Probability.. Hypothesis.. Statistics

Question

1. Testing for name prejudice. When polled, 112 students (n=112) were asked to label/guess the name of a person photoed. 27.7%(31) said Bob, 72.3% (81) said Tim. What are the null and alternative hypothesis? What is the probability that such a proportion (that given in the previous results) could happen purely by chance? Based on data findings, determine whether to reject your Ho (null hypothesis).

Answer 1

σ = sqrt[ P * ( 1 - P ) / n ]

test stat is (p-P)/σ

σ = sqrt( 0.5 * (1-0.5)/ 112]=0.0472455591261534+

the test stats are (0.277 - 0.5)/σ = -4.7190183...

(0.723 - 0.5)/σ = 4.72002...

REJECT the null hypothesis, as there is strong statistical evidence of bias, as expected