Answers
Answer 1
The critical values t₀ for a two-sample t-test is ± 2.0.6
To find the critical values t₀ for a two-sample t-test to test the claim that the population means are equal (i.e., µ₁ = µ₂), we need to use the following formula:
t₀ = ± t_(α/2, df)
where t_(α/2, df) is the critical t-value with α/2 area in the right tail and df degrees of freedom.
The degrees of freedom are calculated as:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
n₁ = 14, n₂ = 12, X₁ = 6,X₂ = 7, s₁ = 2.5 and s₂ = 2.8
α = 0.05 (two-tailed)
First, we need to calculate the degrees of freedom:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
= (2.5²/14 + 2.8²/12)² / [(2.5²/14)²/13 + (2.8²/12)²/11]
= 24.27
Since this is a two-tailed test with α = 0.05, we need to find the t-value with an area of 0.025 in each tail and df = 24.27.
From a t-distribution table, we find:
t_(0.025, 24.27) = 2.0639 (rounded to four decimal places)
Finally, we can calculate the critical values t₀:
t₀ = ± t_(α/2, df) = ± 2.0639
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Related Questions
Instructions: Find the missing probability.
P(B)=1/2P(A|B)=11/25P(AandB)=
Answers
We can use the formula:
P(A and B) = P(B) x P(A|B)
We are given:
P(B) = 1/2
P(A|B) = 11/25
Substituting these values into the formula, we get:
P(A and B) = (1/2) x (11/25) = 11/50
Therefore, P(A and B) = 11/50.
P(A and B) = P(B) x P(A|B)
We are given:
P(B) = 1/2
P(A|B) = 11/25
Substituting these values into the formula, we get:
P(A and B) = (1/2) x (11/25) = 11/50
Therefore, P(A and B) = 11/50.
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