- #1

Mutaja

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## Homework Statement

The following two samples are corrosion values for 20 untreated pipes (X

_{i}) and 20 surface treated pipes (Y

_{i})

∑X

_{i}= 950, ∑X

_{i}

^{2}= 46344 and ∑Y

_{i}= 1092, ∑Y

_{i}

^{2}= 62136

We want to examine if there is basis to claim that the surface treatment reduce corrosion.

a)

1: Find a 95% confidence interval for µ

_{X}- µ

_{Y}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 (X

_{i}), and the other side of the same pipe is left untreated (Y

_{i}). Below is the result.

b)

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.

## Homework Equations

Not sure. Let me know and I will edit this section.

## The Attempt at a Solution

[/B]

I will focus on A for now.

First I need to identify the average corrosion values:

x̅ = ∑X

_{i}/ 20 = 950/20= 47.5

**Ȳ**= ∑X

_{i}/ 20 = 1092/20= 54.6

Then I find the Z value or T value from the tables (not sure which) for 95% confidence interval.

Z

_{0.025}= 1.96

T

_{0.025}= 2.093

Finding the variance:

S

^{2}= 1/19 * Σ(X

_{i}- x̅)

^{2}+ Σ(Y

_{i}-

**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)

=[-132.72, 151.28]

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.