Question

Please interpret. Is there any improvement in process performance from DAY 1-2 to Day 3-4 is significant.

Please interpret. Is there any improvement in process performance from DAY 3-4 to Day 5 is significant.

F-Test Two-Sample for Variances
Days 1&2 /Days 3&4
	3.749530984	3.749
Mean	3.749410833	3.74962
Variance	2.54857E-05	1.05E-05
Observations	287	287
df	286	286
F	2.431579521
P(F<=f) one-tail	7.4211E-14
F Critical one-tail	1.215126558
F-Test Two-Sample for Variances
Days 3&4 / Day 5
	3.749	3.75
Mean	3.749620209	3.750315
Variance	1.04811E-05	6.4E-07
Observations	287	143
df	286	142
F	16.38412609
P(F<=f) one-tail	1.24405E-53
F Critical one-tail	1.277674398

Answer 1

(a)

Based on the given data, we see that the variance of the data for days 3-4 is less than the variance of data for days 1-2.

The p-value obtained for the corresponding F-statistic is 2.43 is equal to 7.42*(10^-14) which is much much less than the conventional significance level of 0.05

So we have to conclude that the decrease in variance is significant. Thus there is improvement in process which is visible as a significant decrease in process variance.

(b)

Based on the exact same reasoning as above, since the F-value is extremely small as compared to 0.05, so the decrease in variance of the process is extremely significant. Hence there is a definite improvement in the process performance from day 3-4 to day 5.