Answer:
Step-by-step explanation:
H0: μ1____ μ2For Q17(circle one: equal to, <u>less than or equal to</u>, greater than or equal to, not equal to )
H1 : μ1____ μ2For Q18(circle one: equal to, less than, <u>greater than</u>, not equal to )
Formula for calculating the the test:
t = [ (x₁ - x₂) - d ] / sqrt[(s₁²/n₁) + (s₂²/n₂)]
where x₁ = 37.6, x₂ = 39.3, d = 0 assuming equality = 37.6 - 39.3 = -1.7
s₁² = 4.92 = 24.01, s₂² = 2.72 = 7.29, n₁ = 50, n₂ = 58.
thus, t = [ (-1.7) - (0)] / √(24.01/50) + (7.29/58)
t = (-1.7) / (0.4802 + 0.1257)
t = -1.7 / 0.6059
t = -2.8057. = -2.81
P value:
Lets find the degree of freedom:
DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }
DF = (24.01/50 + 7.29/58)² / {[(24.01 / 50)² / 50-1)] + (7.29/58)² / 58-1)]}
DF = (0.4802 + 0.1257)² /{[ (0.4802)²/49] + (0.1257)²/57)]}
DF = (0.6059)²/ (0.00471 + 0.00028)
DF = 0.3671 / 0.00499 = 75.37
Thus, P value = 0.9968 using a t distribution calculator.
Decision/Conclusion: Since the P value 0.9968 is greater than α (.05), Fail to Reject H0, There is not sufficient evidence to warrant the rejection of the claim.
