Question

The mean response time of a species of pigs to a stimulus is 0.8 seconds. Twenty-eight pigs were given 2 oz of alcohol and then tested. If their sample average response time was 1.0 seconds with a sample standard deviation of 0.3 seconds, can we conclude that alcohol affects the mean response time? Use the 5 percent significance level.

Answer 1

Answer with explanation:

Let
`\mu` be the mean response time of a species of pigs to a stimulus.

As per given , we have

`H_0 : \mu=0.8\\\\ H_a: \mu\\eq0.8`

Since , the alternative hypothesis is two-tailed and population standard deviation is unknown , so we perform two-tailed t-test.

Also, we have n= 28

Sample mean =
`\overline{x}=1.0`

sample standard deviation= s= 0.3

Test statistic :
`t=\frac{\overline{x}-\mu}{(s)/(√(n))}`

`t=(1.0-0.8)/((0.3)/(√(28)))=3.53`

P-value :
`2P(t>|3.53|)=2(1-P(t\leq3.53))`

`=2(1-0.9992)= 0.0016` [using p-value table for t]

Decision : Since p-value < 0.05 ( significance level ), so we reject the null hypothesis .

Conclusion : We have enough evidence to accept that alcohol affects the mean response time.