According to a company, his lightbulds lasts 4000 hours with a spread of 700 hours.
An institute has tested these lightbulds with a sample size of 100 lightbulbs. They found an average of 3870 hours.
How can be determined if the results clamed by the company are true, based on this sample size alone?
Speculative because the question is unclear, but possibly helpful if I've guessed the meaning correctly.
Test null hypothesis $H_0: \mu = 4000$ vs. $H_a: \mu \ne 4000.$ If 'spread' means $\sigma = 700, n = 100, \bar X = 3879,$ then z statistic for the test is $$Z = \frac{\bar X - \mu_0}{\sigma/\sqrt{n}} = \frac{3879 - 4000}{700/10}.$$ Reject $H_0$ at 5% level if $|Z| \ge 1.96.$
Finish computation, explain why denominator of the z -statistic is $\sigma/\sqrt{n},$ and why we use $1.96.$