Question

COMPLETE USING R!!!

1.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	1100	971	450	892	728
Lab 2	910	878	410	495	1021	980	1002	130	850	620

Test the hypothesis that lab 1 results are higher than that of lab two (a= 0.05).

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

a.What are the null and alternative hypotheses?

b.What is the test statistic and its p-value?

c.What decision and conclusion should you make?

Answer 1

a) Let be the average difference of Lab1 - Lab2.

The null and alternative hypotheses are:

b) Enter data in excel.

Click on Data->Data Analysis and select t-Test: Paired Two Sample for Means

Enter Lab1 data range in variable 1.

Lab2 data range in variable 2.

Hypothesized difference = 0

Click OK

The output is shown below:

The test statistic is:

t = 1.856

For right tailed (one tailed) test, The p-value is:

p-value = 0.0965

c) Since p-value is greater than 0.05, fail to reject the null hypothesis. We can not conclude that lab 1 results are higher than that of lab two.