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

$H_0 : \mu=0.8\\\\ H_a: \mu\neq0.8$

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 : $t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}$

$t=\dfrac{1.0-0.8}{\dfrac{0.3}{\sqrt{28}}}=3.53$

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.