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

Answer:

yes, he was effectively a .400 hitter

Step-by-step 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 = $\sqrt{\frac{y(1 - y)}{n} }$

     = $\sqrt{\frac{0.394(1 - 0.394)}{419} }$

    = 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