Answer :
There is actually enough evidence for the manufacturer to believe that the mean number of hours and mobs will last has actually changed.
We are supposed to use Israel and
significance level α=.05 to perform hypothesis test on the statement of the manufacturer.
So Let's move into our worksheet, our population is 700, our sample size is 48.
The sample mean is 675
Sample standard deviation is 77.
So the first step is to state the null and alternative hypothesis and we have that our hate notes is based on the fact that μ is a cost of 700.
This is what the manufacturer wants, but she thinks that it might have changed probably lesser than or greater than Saddam is our alternative hypotheses, his meal is not equals to 700. So she is not sure whether it does, it's either decrease or increase but it has actually changed.
So after stating our null and alternative protesters, the next needs to state the decision rule that we will be using to either reject or accept the no like protesters.
So will be making a use of the PVA limited to make the decision. It is your roost is that if our evil is better than alpha we are supposed to accept, protesters and if our pivot is lesser than alpha, We are supposed to reject the null hypothesis is that our alpha is equals deserve .05.
So that being said it's time for us to move to draw our test statistics. Now for our test statistic is going to be AT. Test. Yes, our sample size is greater than 30. There's no issue with that. But we actually don't know the value of the population standard deviation. We are making use of the samples and activation which is 27. So that means it would be better if we use our T. Test as our test statistics. So our test statistic is a teacher has given towards us. T is a cost to extra minus meal divided by S divided by the square root of n. Our expert in this case is 6 75 minus. We have 700 divided by our s is 77 divided by the square root of 48. So let's do the math. 6 75 minus 700. We have a -25 divided by so we have 77 divided by the spirit of 48. We have this to be 11.11399. So uh -25 divided by 11.11399. We have our answer to be -2.249. So they simply implies that our test statistics is manners two points 249. So the next step is for us to get the p value attached to this test statistic scenes, we are using the p value method uh to make our decision. So we need a P value. We already have the level of significance. So to get the P value, we can decide to make itself. It it it's a distribution table but that will only give us a range of values in which the p value is located. It won't give us the actual P value. So most times we decide to use calculator to get the p value the exact p value. So our test is actually a two tailed tests were testing for a T score.
Our degree of freedom is the sample size minus one.
48-1=47
And our T score uh is minus two points 249.
So that we have a miners 2.249. And as you can see our p value here is 0.02 0.0294. T. Value is 0.029 so far. Alright, so there's our p value. So the next thing is to make our decision. So we have that as you can see their .0-9 Too far is actually lesser than 0.05 hands.
We make a decision by saying, we are going to reject the null hypothesis. So the decision is that we're going to be rejected the null hypothesis.
As a result, the manufacturer has sufficient reason to think that the average number of hours and mob duration have altered.
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