Question

The CEO of a battery manufacturing company claimed that their batteries would last an average of 280 hours under normal use. A researcher randomly selected 20 batteries from the production line and tested them. The tested batteries had a mean life span of 250 hours with a standard deviation of 40 hours. Do we have enough evidence to suggest that the claim of an average of 280 hours is false?

Answer 1

$H_0:a=280$

$H_1:a<280$

Test statistic: $T={\frac {(X-a)*\sqrt{n}} {\sigma}}={\frac {(250-280)*\sqrt{20}} {40}}\approx -3.35$

Since the sample size is small(<30), then it is appropriate to use t-score as critical value. There is no mention about confidence level, but usually there are 3 types are used: 90%, 95%, 99%. Lets run on 99% confidence level.

So, $P(T(20-1)<Cr)=1-0.99=0.01\implies Cr=-2.539$

Since T<Cr, then we should conclude that, based on the given data, there is enough evidence to reject the null hypothesis and admit that average lifespan is smaller than population's