Answer:
The coin toss does not appear to be fair
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 400[/tex]
The number of game won by team that won the coin toss at the beginning of overtime [tex]x = 194[/tex]
The level of significance is [tex]\alpha = 0.10[/tex]
The population proportion is evaluated as
[tex]p = \frac{194}{400}[/tex]
[tex]p = 0.485[/tex]
Since the population proportion is 0.485 [tex]\approx[/tex] 0.5 which implies that the coin toss is fair then
The Null hypothesis is
[tex]H_o : p = 0.485[/tex]
and The Alternative hypothesis is
[tex]H_a : p \ne 0.485[/tex]
The test statistics is evaluated as follows
[tex]t = \frac{[x + p] - [\frac{n}{2} ]}{\frac{\sqrt{n} }{2} }[/tex]
substituting values
[tex]t = \frac{[194 + 0.485] - [\frac{400}{2} ]}{\frac{\sqrt{400} }{2} }[/tex]
[tex]t = -0.5515[/tex]
=> [tex]|t| = 0.5515[/tex]
now the critical value of [tex]\alpha[/tex] for a two tail test(it is two tailed because we are test whether the critical value is less than or greater than the test statistics ) is
[tex]t_{\alpha } = 1.645[/tex]
This is usually found from the critical value table
Now comparing the critical values and the calculated test statistics we see that the critical value is greater than the test statistics hence the Null hypothesis is rejected
This means that the coin toss is not fair
