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Bacteria in water are counted as colony-forming units (CFU’s) per milliliter. Te

ID: 3135123 • Letter: B

Question

Bacteria in water are counted as colony-forming units (CFU’s) per milliliter. Ten bottles of water are randomly selected for sampling, with the intention of testing if two different labs produce the same results. Each bottle is divided into two parts, and then given to each of the two labs:

Bottle

1

2

3

4

5

6

7

8

9

10

Lab 1

875

959

475

589

925

1200

971

421

892

728

Lab 2

910

878

480

495

1021

980

1002

410

850

620

A) What is the probability that the average sample mean from lab 1 is more than 59 CFU’s larger than that of lab 2?

B) What is the probability that the average sample mean from lab 2 is more than 42 CFU’s larger than that of lab 1?

HINT: are the ten observations from lab 1 independent of those from lab 2?

Bottle

1

2

3

4

5

6

7

8

9

10

Lab 1

875

959

475

589

925

1200

971

421

892

728

Lab 2

910

878

480

495

1021

980

1002

410

850

620

Explanation / Answer

Lab1 : {875,959,475,589,925,1200,971,421,892,728}

SD1 = 245.64

Mean1 = 803.5

Lab2 : {910,,878,480,495,1021,980,1002,410,850,620}

SD2 = 238.07

Mean2 = 764.6

Standard Error (SE) = sqrt( (SD1^2/n1) + (SD2^2/n2) )
= sqrt( ((245.64)^2/10) + ((238.07)^2/10) )
= 108.174

A)
t = [ (Mean1 - Mean2) - d ] / SE
= ((803.5-764.6)-59)/108.174
= -0.185

dF =10+10-2 = 18

P-value = 0.5723 Answer


B)
t = [ (Mean2 - Mean1) - d ] / SE
= ((764.6-803.5)-42)/108.174
= -0.747

dF =10+10-2 = 18

P-value = 0.7676 Answer

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