Week 16: Hypothesis Testing

 Welcome back to my blog~!

This week, we went through hypothesis testing. This is basically to put an assumed relationship to the test through hard evidence (i.e data!) and see the alternatives.

We were tasked to investigate whether 2 manufactured catapults, A and B, would have the same flying distance. We previously talked about the three specific factors taken from our DOE experiment, which is arm length, start angle and stop angle.

For our team, we split it to the following:

I would compare run #3 from full factorial (as catapult A's data) to run #3 from fractional factorial (as catapult B's data).

Nigel would compare run #2 from full factorial (as catapult A's data) to run #2 from fractional factorial (as catapult B's data).

Vernon would compare run #5 from full factorial (as catapult A's data) to run #5 from fractional factorial (as catapult B's data).

Madelaine would compare run #8 from full factorial (as catapult A's data) to run #8 from fractional factorial (as catapult B's data).

In this test, we can assume that human factor is negligible, thus different users won't have an effect on flying distance.

For my test, the settings of both catapults are listed below:

Arm length = 25cm

Start angle = 0 degrees

Stop angle = 60 degrees

For my null hypothesis, both catapult A and catapult B have the same mean flying distance. This means that the flying distance made from catapult A is equal to the flying distance made from catapult B (Da = Db).

For my alternative hypothesis, catapult A and catapult B do not have the same mean flying distance This means that the flying distance made from catapult A is not equal to the flying distance made from catapult B(Da /= Db).

Here is the data for catapult A:

and... for catapult B:

Based on this, we have a sample size of 16 which is less than 30, hence t-test will be used.

Since the sign is /=, a two-tailed test is used, and significance level (a) is 0.05.

The mean and standard deviation of catapult A and B are shown here:

Catapult A - Ma = 95.3cm, Sa = 2.66cm

Catapult B - Mb = 96.6cm, Sb = 3.11cm

Using the t-test equations,

Hence, t = -0.84 (2d.p).

At 0.05 significance level for two-tailed, v = 14, t0.975 = +-2.145.

With +t0.975 > t > -t0.975, it lies in the acceptance region, hence, through using the t-test, the null hypothesis is supported and hence the catapult A and catapult B are manufactured the same and therefore the manufacturing is consistent.

When I saw my other teammate's t values, theirs wasn't acceptable. With different high set values, this could infer that the arm length and start angle has a much more significant and vapid effect on the flying distance than stop angle.

Through these data analyses, I find that there is a relationship with the t values to the null hypothesis. For this run my data was the only one that would be acceptable, while the rest had unacceptable results. Hence, it is definitely a matter of seeing a larger picture rather than just the one comparison. I find that the calculations itself takes some getting used to and the method of using calculation to test a hypothesis is quite new to me. Some practice would be needed to internalise all of these.

Thank you for reading!