Question

Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 42 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using MINITAB, resulting in the accompanying output.

Variable	N	Mean	StDev	SEMean	Z	P-Value
lifetime	42	738.44	37.68	5.81	−1.99	0.023

What conclusion would be appropriate for a significance level of 0.05?

Reject the null hypothesis. There is not sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours.Reject the null hypothesis. There is sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours.    Do not reject the null hypothesis. There is not sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours.Do not reject the null hypothesis. There is sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours.

What conclusion would be appropriate for a significance level of 0.01?

Do not reject the null hypothesis. There is sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours.Do not reject the null hypothesis. There is not sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours.    Reject the null hypothesis. There is not sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours.Reject the null hypothesis. There is sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours.

What significance level and conclusion would you recommend and why?

Answer 1