# Hypothesis Testing

• Oct 25th 2010, 11:35 PM
lpd
Hypothesis Testing
Hi I have this question.

If $\displaystyle 26$ of $\displaystyle 200$ tyres of $\displaystyle brand A$ failed to last $\displaystyle 20,000$ miles, while the corresponding gures for $\displaystyle 200$ tires of$\displaystyle Brands B$, $\displaystyle C$, and $\displaystyle D$ were $\displaystyle 23$, $\displaystyle 15$ and $\displaystyle 32$, test the null hypothesis that there is no di erence in the quality of the four kinds of tyres.
Use $\displaystyle \alpha = 0.05$.

Thank-you so much!
• Oct 26th 2010, 02:35 AM
CaptainBlack
Quote:

Originally Posted by lpd
Hi I have this question.

If $\displaystyle 26$ of $\displaystyle 200$ tyres of $\displaystyle brand A$ failed to last $\displaystyle 20,000$ miles, while the corresponding gures for $\displaystyle 200$ tires of$\displaystyle Brands B$, $\displaystyle C$, and $\displaystyle D$ were $\displaystyle 23$, $\displaystyle 15$ and $\displaystyle 32$, test the null hypothesis that there is no dierence in the quality of the four kinds of tyres.
Use $\displaystyle \alpha = 0.05$.

Thank-you so much!

What have you done? What specific difficulties do you have with this question?

The null hypothesis is that there is no difference.

CB
• Oct 26th 2010, 03:21 AM
lpd
What kind of test should I use for this particular distribution?
• Oct 26th 2010, 05:58 AM
CaptainBlack
Quote:

Originally Posted by lpd
What kind of test should I use for this particular distribution?

The number of failure in 200 trials with a given probability p has a binomial distribution B(200,p), which you can probably approximate in this case by a normal. You now need to find an interval such that the probability of none of four observations from this distribution are out side is 5%.

CB