What is the 95% confidence interval for the Gila River sample of loach minnows given: mm,s = 6.2 mm,n = 50,and critical value of t = 2.01.
A) 56.2 mm + 1.77 mm
B) 56.2 mm $\pm$ 1.77 mm
C) 56.2 mm - 2.26 mm
D) 56.2 mm $\pm$ 0.25 mm
E) 56.2 mm + 0.25 mm

Question

What is the 95% confidence interval for the Gila River sample of loach minnows given:  mm,s = 6.2 mm,n = 50,and critical value of t = 2.01.
A) 56.2 mm + 1.77 mm 
B) 56.2 mm $\pm$ 1.77 mm 
C) 56.2 mm - 2.26 mm 
D) 56.2 mm $\pm$ 0.25 mm 
E) 56.2 mm + 0.25 mm

Quizplus · Accepted Answer

The formula for the confidence interval is:
CI = x̄ ± t*s/√n
where x̄ is the sample mean, t is the critical value from the t-distribution table at 95% confidence level and 49 degrees of freedom (n-1), s is the sample standard deviation, and n is the sample size.

Plugging in the values given in the question:
x̄ = 56.2 mm
s = 6.2 mm
n = 50
t = 2.01

CI = 56.2 ± 2.01(6.2)/√50
CI = 56.2 ± 1.77

So the 95% confidence interval for the loach minnows is 56.2 mm ± 1.77 mm, which is choice B.

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What Is the 95% Confidence Interval for the Gila River $\pm$