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Sagot :
The confidence interval for the difference between the average salaries of male and female neurologists is (19,131.77, 36,868.23). And the formula which should be used to compute the interval is x₁` - x₂`/ Sp √ (1/n₁ + 1/n₂).
The 99% confidence interval for the difference between the average salaries of male and female neurologists is given by:
(x₁` - x₂`) ± t∝/2(υ) * √ (Sp²/n₁ + Sp²/n₂)
= x₁` - x₂`/ Sp √ (1/n₁ + 1/n₂)
where Sp² = s₁² (n₁ - 1) + s₂² (n₂ - 1) / (n₁ - 1) + (n₂ - 1)
The sample should be normally distributed, and it is assumed that the population standard deviations are known, which is sometimes met and sometimes not known.
Now, we have H0 : μ₁ = μ₂ against the claim Ha : μ₁ ≠ μ₂.
And the test statistic is:
t = x₁` - x₂` / √ (Sp²/n₁ + Sp²/n₂)
Sp² = s₁² (n₁ - 1) + s₂² (n₂ - 1) / (n₁ - 1) + (n₂ - 1)
= 15,000² (17) + 22,000² (22) / 37
= 103,378,640
Now, degree of freedom (df):
df = n₁ + n₂ - 2 = 21 + 18 - 2 = 37
For 2-tailed-test, the critical value of t is obtained by:
t ≥ t∝/2 (df) = t ≥ t0.005 (37) = ± 2.7154 = ± 2.72
Last, insert the values to the formula:
(x₁` - x₂`) ± t∝/2(υ) * √ (Sp²/n₁ + Sp²/n₂)
= 28,000 ± (2.72 * 3,265.89)
= (19,131.77, 36,868.23)
Hence, the confidence interval is (19,131.77, 36,868.23).
Learn more about confidence interval at: https://brainly.com/question/24131141
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