Question

A manufacturer claims that the mean lifetime, u, of its light bulbs is 50 months. The standard deviation of these lifetimes is 8 months. Fifty bulbs are selected at random, and their mean lifetime is found to be 49 months. Can we conclude, at the 0.1 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 50 months?

Answer 1

Solution:

Given in the question

Claim is that the mean lifetime of light bulbs made by this manufacturers differs from 50 months so null hypothesis and alternative hypothesis can be written as follows:

Null hypothesis H0: = 50 months

Alternate hypothesis Ha: 50 months

Population standard deviation = 8 months

No. Of sample = 50

Sample mean = 49 months

Here we will use Z test because sample size is large enough and population standard deviation is known.

So test statitsic can be calculated as

Test statistic = (Sample mean - )//sqrt(n) = (49-50)/8/sqrt(50) = -1/1.13 = -0.88

So P-value can be found from Z table

As this is two tailed test so P-value = 0.3789

At alpha= 0.1, we are failed to reject the null hypothesis because p-value is greater than alpha value so we have don't have significant evidence to support the alternative claim that is mean life of bulb differs from 50 months.