Question

Find an example of application of Hypothesis testing that you can relate to (any example would be OK using Z test you can consult HW Batch No. 4 or textbook). Show all five steps of Hypothesis testing with numerical example (you can use fictitious numbers if you have to). And find the P-Value and re-affirm Step 4 with P-Value.

Answer 1

Appications of Hypothesis testing using an Z-test.

Suppose that 100 high performance tires made by a certain manufacturer lasted on the average 21819 miles with a standard deviation of 1295 miles. Test the null hypthesis miles against the alternative hypothesis at the 0.05 level of significance.

Soltion:

1. Let us assume hat the performance of tires follows a normal distribution and the tires taken are all random or independent.

2. Null and alternate Hypothesis:

Level of significance:

3. Critical region: Reject the null hypthesis if Z<-1.645, where

4. Substituting , we get

  

  

  

5. since the z=-1.3977 is greater than -1.645, teh null hypothesis cannot be rejected; theer is no convincing evidence that the tires are not as good as assumed under the null hypothesis.