Question

Before a strike prematurely ended the 1994 major league baseball season, Tony Gwynn of the San Diego Padres had 165 hits in 419 at bats, for a .394 batting average. Baseball fans argued over whether Gwynn was effectively a .400 hitter that year. Test this hypothesis

Answer 1

yes, he was effectively a .400 hitter

Explanation:

The mean rate of success ( ÿ ) is 0.394.

The total number of hits was 419.

Under table t the value at 5% confidence interval is 1.96.

Here se the asymptotic standard deviation is given as follows

se =
`\sqrt{(y(1 - y))/(n) }`

=
`\sqrt{(0.394(1 - 0.394))/(419) }`

= 0.02387

The confidence interval is calculated as follows:

y ± 1.96 * se

0.394 ± 1.96 * 0.02387

the answer is -0.347 or 0.4407)

meaning that the mean lies between -0.347 to 0.4407.

There is strong evidence that 0.4 lies between the above confidence interval.

This means that Gwynn was effectively a 0.4 hitter