00:01
For this problem to begin, we know that the company's claim is that the mean lifespan of the batteries is equal to 48 hours.
00:09
Since that's a statement of exact equality, that will become our null hypothesis.
00:13
Our alternative hypothesis will be the exact negation of that, that the mean value differs from 48 hours.
00:22
So we know that the consumer rights group took a sample, found a sample mean of 47 hours, a sample standard deviation of 3 hours, for a sample of size 30.
00:39
Now i'll note that the population standard deviation is unknown, so it's going to be appropriate to do this test here as a two -tailed t -test.
00:52
We know that we're testing at the 0 .05 level of significance, so our critical value, which is 29 degrees of freedom, is a one -tailed proportion of 0 .025.
01:10
I'll find that critical t -value using my t -distribution table over here.
01:15
We want one tail, 0 .025, wanted 29 degrees of freedom.
01:23
We can see that our critical t -value is 2 .045.
01:31
So that means that we will reject the null hypothesis if the magnitude of our observed t -score is greater than 2 .045...