Question

Using the raw data from each trial perform a T-test comparing results from one variable group to another variable ( 6hr vs overnight ) and determine the p-value for the comparison. Report whether or not there was a statistically significant difference between the results when comparing the two variable.

Overnight E. coli Host	6hr E. coli Host
2.71 x 10^9 PFU/ml	3.04 x 10^9 PFU/ml
3.11 x10^9 PFU/ml	2.58 x 10^9 PFU/ml
3.1 x 10^9 PFU/mL	2.99 x 10^8 PFU/ml

Answer 1

> In order to compare pesults from one variable group to another variable (Ghr vs overnight using t-test, we are going to test the difference of the two means. Let us consider Ghr' gooup as population 1 having and population mean and Overnight variable group as population. 2 having mean U2: ug and i are unknown.. The null and the alternative hypothesis is given by Ho: M1-=0 Against H1: 41-42 70 we are using a to tailed t-test. The test statistic is given by : T (x1 - x2) n t notna-2 S'= pooled variance of two samples = (01-15 2+ (02-1) 522 niton 2-2 Here, Population 1 Population 2 sample mean - Ri= 1/1 72 = /ng sample variance -> (-73)* $ 13(x8; -73) sample size ni na For the given data, we have ny = 3=na x= (2.91+ 3.11 + 3.1) x103 - = 2.973 X 109 (overnight) = (3.04+ 2.58 +2.99*10- 2.89x109 Sa = 0.0520 x 108 0 (2.41 -2-943)*10*3# {(15-31-2-978) x 10°37 {(13.10-2.975)x 10932 [{(15-04-2-81) X10°}} {(2-58-2-87)x10°3* {(2.99-2.84)x109}] sa = 0.0637 x 1018 S 2 x 1018 [0-0520 + 0.0637] = 0.05785 x 1018 .. s'= 0.2405202694 0.2405 x 10 X105

:.T(2-87-2.973)x10° 0.2405) 0-2405 x 10 (-0. 103) 0-2405 /213 = – 0.5245 For a two tailed I testowe need to compare the P-value of IT = 0.5245 with desined level of o. let d = 0.05, from t- table we can see that, for df=4, thene is no exact value given but a=0. Ohas the value 0.741 which mean P-value corresponding to T=0.5245 will be some where between 1.00 and 0.50 which is greater than our desired level of d. Hence, it indicates weculo insufficent evidence against the null hypothesis to be incorrect. So, we accept the null hypothesis. Also, we say that, thepe is no statistically significant diffenence best between the pesults.