Question

2) An experiment is conducted to determine if the mean values are equal or not equal for a P process, The following data on the mean life of the P process are sampled using Pl & P2 samples and the times to failure are indicated as follows: Test the hypothesis at the 5% significance level, that the mean values are equal ? P1 P2 a). What type of statistical test would you apply to test the hypothesis? b) State the Null hypothesis clearly c) State the Alternative or Research Hypothesis clearly d) State clearly the test statistic e) State the decision criteria based on the critical test statistic value f) Draw the statistical distribution and specify the acceptance and rejection regions g) What would you conclude about the equality of mean values for this test ?

Answer 1

Answer

a) What type of Statistical test would you apply to test the hypothesis.

2 Sample t test need to be used to test the hypothesis as sample size is less, and we want to test  two population means to determine whether they are significantly different and standard deviations are unknown and samples are drawn independently from each other.

b) State the Null Hypothesis clearly

Null Hypothesis : H₀ : µ_P1- µ_P2 = 0 i.e There is no difference between mean values for P1 and P2

c) State the alternate or Research Hypotheis clearly

Alternate Hypothesis : Ha : µ_P1- µ_P2 <> 0 i.e There is   difference between mean values for P1 and P2

d) State clearly the test statistic

test statistic   

t =( (X_p1bar - X_p2bar) - ?)/(S_p*SQRT(1/n_p1 + 1/n_p2))

where ? is hypothesized difference of mean ,( ?=0 in this case)

S_p = Pooled Standard Deviation is determined by the following formula :

S_p²=( ( n_p1-1) S_p1² + ( n_p2-1) S_p2² )/( n_p1 + n_p2 – 2)

S_p1 and S_p2 are standard deviation of p1 and p2 respectively

Calculation of test statistic :

	P 1		P2
	2		3
	2		4
	3		6
	2		5
	2		6
	3		6
			7
XP1bar	2.333	XP2bar	5.286
Sp1	0.516	Sp2	1.380
np1	6	np2	7
Sp =	=SQRT(=( ( np1-1) Sp12 + ( np2-1) Sp22 )/( np1 + np2 – 2)
=	0.3248
test statistic
	-5.057715091

e) State the decision criteria based the critical test statistic value

Critical test statistic value whre alpha =0.05 , degrees of freedom (df )= np1 +np2-2 =6+7-2=11

t_0.05 for df 11 is 2.20

hence Decision Criteria :

Reject the null Hypothesis H₀  if t<-2.20 or t >2.20   

f) Draw the statistical Distribution and specify the acceptance and rejection region.

Acapte Rejech

g) What would you conclude about the equality of means

Conclusion : Means of P1 and P2 are not the same.