In a psychology experiment in which 100 volunteers were asked to read a paragraph about an engineer, 65 assumed that the engineer was male despite the fact that the paragraph did not specify gender (and avoided gendered pronouns such as “he” or “she”). If the null hypothesis here is that there is no gender bias, what is the two-sided p-value associated with this result? Use a normal approximation to solve this.

P=.0001 p=.003 p=.10 p=.05 p=.99

Question

In a psychology experiment in which 100 volunteers were asked to read a paragraph about an engineer, 65 assumed that the engineer was male despite the fact that the paragraph did not specify gender (and avoided gendered pronouns such as “he” or “she”). If the null hypothesis here is that there is no gender bias, what is the two-sided p-value associated with this result? Use a normal approximation to solve this.

P=.0001 p=.003 p=.10 p=.05 p=.99

anonymous · Answer

The null hypothesis should be:
Ho:p=0.5 (no bias, which means 50% of the population would say "male" and the other 50% would say "female")
Ha:p<>0.5 

We approximate null hypothesis with a normal distribution:
$$\mu=np=100·0.5=50$$$$\sigma=\sqrt{n·p·(1-p)}=\sqrt{100·0.5·0.5}=5$$Assuming Ho is true$$P_{VALUE}=1-P(35 \le x \le 65)=1-P(-3 \le z \le +3)=$$$$=1-0.9973=0.0027\approx 0.003$$