The following two samples are corrosion values for 20 untreated pipes (Xi) and 20 surface treated pipes (Yi)
∑Xi = 950, ∑Xi2 = 46344 and ∑Yi = 1092, ∑Yi2 = 62136
We want to examine if there is basis to claim that the surface treatment reduce corrosion.
1: Find a 95% confidence interval for µX - µY based on the samples above. Be clear as to which assumptions you have done. Does the surface treatment reduce the corrosion?
2: Perform a hypothesis test with significance level 5%. Again be clear as to which assumptions you've done to use this test.
A new test is being done on 20 different pipes. This time the test is done by using the surface treatment on one side (Xi), and the other side of the same pipe is left untreated (Yi). Below is the result.
Do a hypothesis test regarding the surface treatment reducing corrosion. Again use significance level 5%. Be clear as to which assumptions you have done to use this test.
Not sure. Let me know and I will edit this section.
The Attempt at a Solution
I will focus on A for now.
First I need to identify the average corrosion values:
x̅ = ∑Xi / 20 = 950/20= 47.5
Ȳ = ∑Xi / 20 = 1092/20= 54.6
Then I find the Z value or T value from the tables (not sure which) for 95% confidence interval.
Z0.025 = 1.96
T0.025 = 2.093
Finding the variance:
S2 = 1/19 * Σ(Xi - x̅)2 + Σ(Yi - Ȳ)2
I calculated this manually to be 196.41.
Which then gave me the confidence interval: 950 - 1092 +/- 2.093*√(196.41) * √(1/20 + 1/20)
Where am I going wrong, and how do I use the numbers I get for my confidence interval to draw a conclusion?
PS: I remember for way back when using this forum that there was a much easier way of typing formulas properly. And the problem is translated from Lithuanian so please let me know if something is unclear.