Questions :
a. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 100. (Round your answer to four decimal places.)
b. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 500. (Round your answer to four decimal places.)
c. Is the small P-value for n = 500 indicative of a difference that has practical significance
Answer :
0.1574
0.00157
Yes
Explanation:
Hypothesis :
H0 : μ1 - μ2 = 0
H1 : μ1 - μ2 ≠ 0
Given :
x1 = 60.7 ; x2 = 60.5 ; s1 = 1 ; s2 = 2
Based on n = 100
Test statistic, Z :
Z = (x1 - x2)/[√(s1²/n1 + s2²/n2 )]
x1 - x2 = 60.7 - 60.5 = 0.2
0.2 / √(1²/100 + 1²/100 )]
0.2 / √0.02
Z = 1.414
The Pvalue from Zscore :
P(Z < 1.414) = 0.1574
B.)
For n = 500
Z = (x1 - x2)/[√(s1²/n1 + s2²/n2 )]
x1 - x2 = 60.7 - 60.5 = 0.2
0.2 / √(1²/500 + 1²/500 )]
0.2 / √0.004
Z = 3.162
The Pvalue from Zscore :
P(Z < 3.162) = 0.00157
Yes, the small Pvalue for n = 500 is indicative of a difference with practical significance ; as the Pvalue are compare with the α to make about a Decison about our hypothesis.