SOLUTION: Independent random samples of n1 = 18 and n2 = 13 observations were selected from two normal populations with equal variances.
DATA:-
___________ ______Population (IGNORE the li
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Question 1207925: Independent random samples of n1 = 18 and n2 = 13 observations were selected from two normal populations with equal variances.
DATA:-
__________________Population (IGNORE the lines - represents space)
__________________1______2 (IGNORE the lines - represents space)
Sample Size______18______13 (IGNORE the lines - represents space)
Sample Mean_____34.6_____32.1 (IGNORE the lines - represents space)
Sample Variance__4.5_____5.9 (IGNORE the lines - represents space)
(a) Find the rejection region for the test in part (a) for 𝛼 = 0.01. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)
t > _________
t < _________
(b) Find the value of the test statistic. (Round your answer to three decimal places.)
t = _________
Answer by textot(100) (Show Source): You can put this solution on YOUR website!
**a) Find the rejection region for the test in part (a) for 𝛼 = 0.01.**
* **Degrees of Freedom:**
* df = n1 + n2 - 2 = 18 + 13 - 2 = 29
* **Critical t-values:**
* Since it's a two-tailed test with α = 0.01, we need to find the critical t-values that split the distribution into the middle 98% and the two 1% tails.
* Using a t-distribution table or a calculator (like Python's scipy library), we find:
* t > 2.756
* t < -2.756
**b) Find the value of the test statistic.**
1. **Calculate Pooled Variance:**
* s_pooled^2 = ((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2)
* s_pooled^2 = ((18 - 1) * 4.5 + (13 - 1) * 5.9) / (18 + 13 - 2)
* s_pooled^2 = 5.14
* s_pooled = √5.14 ≈ 2.267
2. **Calculate t-statistic:**
* t = (x̄1 - x̄2) / (s_pooled * √(1/n1 + 1/n2))
* t = (34.6 - 32.1) / (2.267 * √(1/18 + 1/13))
* t ≈ 3.048
**Therefore:**
* **Rejection Region:** t > 2.756 and t < -2.756
* **Test Statistic:** t = 3.048
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