Question

In a survey of 100 people who play chess against a computer player, it was found that the computer won 90 percent of the matches. Is there statistical significance to say that the computer is a better chess player than the people who played against it?

These are the choices

No, because the results are likely to occur by chance.

Yes, because a computer will always win in a competition against a human.

Yes, because the results are unlikely to occur by chance.

No, because the sample is a voluntary sample of those people willing to play against a computer.

Answer 1

Yes, because the results are unlikely to occur by chance. The computer isn't going to make a mistake and play at the best it can. So every time it wins it is because it is better and when it loses its because the human was better, not by chance.

Answer 2

Option b is right

Explanation:

Sample size =100

p = sample proportion of computer winning = 0.9

q = sample proportion of computer not winning = 0.1

P = the population proportion

If equally likely then P = 0.5

H0: p =0.5

Ha: p>0.5

(One tailed test)

Test statistic =
`\frac{p-P}{\sqrt{(pq)/(n) } } \\=(0.4)/(0.03) \\=13.33`

Since this lies outside 1.96 we reject null hypothesis

i.e. computer will always win in a competition against humna

Option b is right