In 625 at bats a baseball player got a hit 28% of the time. Find a...

In 625 at bats a baseball player got a hit 28% of the time. Find a 95% confidence interval for the true percentage of time he gets a hit.

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Expert Solution

Solution :

Given that,

n = 625

Point estimate = sample proportion = = 0.28

1 - = 1-0.28=0.72

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z / 2 * $\sqrt$ (( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((0.28*0.72) / 625)

E = 0.0352

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.28-0.0352 < p < 0.28+0.0352

0.2448< p < 0.3152

The 95% confidence interval for the population proportion p is : 0.2448, 0.3152

orchestra answered 1 year ago

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