The qualitycontrol manager at light bulb factory needs to de

The quality-control manager at light bulb factory needs to determine whether the mean lifew of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.

At the 0.05 level of significance, is there evidence that the mean lifew is different from 375 hours?

Solution

Ho = mean is 375
Ha = mean is not 375
alpha = 0.05
Test statistic is z =(xbar-mean)/100/(sqrt(64))

critical value is |z|>1.96
calculation is z=25*8/100=+2

Since the key word \"different\" is the question, then this is a two-tailed test. Therefore, divide 0.05 by 2 = .025(per tail). We find the critical values by going to the z-score tables for normal distribution. Notice that the area= .025 corresponds to z-scores(critical values)= ±1.96. To calculate test-statistic manually: (350-375)/(100/64) =-25/12.5= -2 .

Reject Ho. There is a significant difference in the mean life of the population of light bulbs.