Question

a laptop manufacturer claims that the latest model of laptop will last an average of 10 hours under normal use.A researcher randomly selects 25 laptops of the latest model form the company and tested these laptop have mean lifespan of 8.5 hours and standard deviation of 3,7 hours ,does the company have enough evidence that their claim is true at 1% level of significance

Answer 1

$t=\frac{\overline{x}-\mu}{\sigma/\sqrt{n}}=\frac{8.5-10}{3.7\sqrt{25}}=0.081$

$df=n-1=25-1=24$

Critical value:

two tails $t_{.995}=2.797$

Since |t| < critical value, we can conclude that company's claim is true.