Question

Consider the hypothesis statement to the right using alphaequals0.01 and the data to the right from two independent samples. ​a) Calculate the appropriate test statistic and interpret the result. ​b) Calculate the​ p-value and interpret the result. Click here to view page 1 of the standard normal table. LOADING... Click here to view page 2 of the standard normal table. LOADING... H0​: mu1minusmu2less than or equals0 H1​: mu1minusmu2greater than0 x overbar1 equals 88 x overbar2 equals 82 sigma1 equals 24 sigma2 equals 20 n1 equals 45 n2 equals 55 ​a) The test statistic is nothing. ​(Round to two decimal places as​ needed.)

Answer 1

Solution

Hypotheses:

Null: H₀: (µ1 - µ2) ≤ 0   Vs Alternative: H₁: (µ1 - µ2) > 0

Test Statistic:

Z = (X₁bar – X₂bar)/√{(σ₁²/n₁)+(σ₂²/n₂)} = 1.34

where

X₁bar and X₂bar are sample averages based on n₁ observations on X₁ and n₂ observations on X2

σ₁, σ₂ are respective population standard deviations.

Calculations

Summary of Excel calculations is given below:

n1	45
n2	55
X1bar	88.00
X2bar	82.00
σ1	24
σ2	20
σ12	576
σ22	400
Zcal	1.339208
α	0.01
p-value	0.090251
σ12/n1	12.8
σ22/n2	7.272727
Sum	20.07273
Sqrt	4.48026
1- α	0.99

Distribution, and p-value:

Under H₀, Z ~ N(0, 1),

Hence, p-value = P(Z > Zcal).

Using Standard Normal Table, the p-value is found to be as shown in the above table:

Decision:

Since p-value > α, H₀ is accepted.

Conclusion:

There is not sufficient evidence to suggest that the difference between the two population means is greater than zero. Answer

DONE