Question

In 2011, The New York Yankees won 97 out of 162 of their baseball games. Is there sufficient evidence that the proportion of wins is greater than 0.5 at the α = 0.10 significance level?

Answer 1

Answer: It is sufficient evidence that it will reject the null hypothesis.

Explanation:

Since we have given that

Number of players of baseball games = 162

Number of games won = 97

So,
`\hat{p}=(97)/(162)=0.5988`

Hypothesis:

`H_0:p\leq 0.5\\\\H_a:p>0.5`

So, test statistic would be

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\\\z=(0.5988-0.5)/(\sqrt(0.5* 0.5)/(162))}\\\\z=2.514`

And the p-value = 0.006 at z=2.514.

Since p-value < α = 0.10 significance level.

Hence, it is sufficient evidence that it will reject the null hypothesis.