{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CEE 202 Homework 11 solution

# 0920 3707 2 309902 19584 8 3822 1419 cee

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: .59 195.84 376479.50 38.22 3764.13 Average 448.25 4.44 Sum 5762.35 n ∑ (V − V ) ( pH i b= i − pH i =1 n ∑ ( pH i =1 i − pH ) ) 2 = 3764.13 = 98.4867 38.22 a = V − b pH = 448.25 − 98.4867 × 4.44 = 11.0920 The linear relationship between output voltage and pH is: pH=11.0920+98.4867V 800 Output Voltage (mv) 700 600 Orignial Data 500 Linear (Orignial Data) 400 300 200 100 0 0 2 4 pH 6 8 13/19 CEE 202 – Engineering Risk & Uncertainty Spring 2011 (Bond) Homework 11 Diff. between Means; Least ­Squares b) What is a 99% confidence interval for those coefficients? From the table above, we can get n 2 2 SST = ( n − 1) SV = ∑ (Vi − V ) = 376479.50 , i =1 n 2 ( n − 1) S pH = ∑ ( pH i − pH ) 2 = 38.22 , i =1 n ∑ (V − V ) ( pH i ) − pH = 3764.13 , i i =1 n s= n 2 ( ∑ (Vi − V ) − b∑ (Vi − V ) pH i − pH i =1 i =1 ) n−2 376479.50 − ( 98.4867 ) × (3764.13 ) 8−2 = 30.9902 Or you can use SSE 5762.35 s= = = 30.9902 n−2 6 α = 1 − 0.99 = 0.01 , in each tail α 2 = 0.005; d.f.=n ­2=8 ­2=6 Using Table A4. or function tinv in Excel, we find that t0.005 = 3.707 for 6 degrees of freedom. Therefore, a 99% confidence interval for b is s 30.9902 β = b ± tα /2 = 98.4867 ± 3.707 × = n 2 38.22 ∑ pH i − pH = i =1 ( ) 98.4867 ± 18.5846or ( 79.9021,117.0714) From the table above, we can also get n ∑ pH 2 i = 195.84 , i =1 A 99% confidence interval for a is s α = a ± tα 2 n ∑ pH 2 i i =1 n ( n∑ pH i − pH i =1 = 11.0920 ± 3.707 × 2 ) 30.9902 195.84 = 8 × 38.22 14/19 CEE 202 – Engineering Risk & Uncertainty Spring 2011 (Bond) Homework 11 Diff. between Means; Least ­Squares 11.0920 ± 91.9515 or ( −80.8595,103.0435) c) Your labmate says, “This slope is very small. I don’t think your analyzer is working.” How do you answer? If the analyzer is working, it means that the ou...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern