Question

Average life of light bulbs produced by SABA Electric Co. is believed to be normally distributed with the mean service life of 1200 hours and a standard deviation of 78 hours. A random sample of 169 bulbs is tested and it has a mean life of 110 hours. Can we conclude that the mean service life of the bulbs is less than the expectation at 98% level of confidence?

a. Yes. The mean service life of the bulbs is less than the expectation.

b. No. The mean service life of the bulbs is not less than the expectation.

c. Both a and b are correct.

d. None of the above.

Answer 1

Here we have and and n= 169.

The null and alternate hypothesis are :

There is no difference between the mean service life and the expectation;

The mean service life of bulbs is less than the expectation;

Since we are asked to conclude it at 98% level of confidence so the level of significance i.e. for this level of confidence will be : 1 - level of confidence/100 = 1 - 0.98 = 0.02

Now

Hence

Now from the table below we will find the tabulated t-value for 0.02 level of significance (for large value) :

Hence

Since the calculated value > tabulated value hence the null hypothesis will be rejected. Then YES, THE MEAN SERVICE LIFE OF THE BULBS IS LESS THAN THE EXPECTATION (A).