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unknown mean μ
yielded x¯
x
¯
= 123 and s = 28. Assume σ
σ
= 25. Construct a 90% confidence interval for

Sagot :

raphealnwobi

Answer:

The answer is below

Explanation:

The question is not complete, but I will solve a similar question. The question goes as:

A random sample of n measurements was selected from a population with unknown mean µ and known standard deviation σ. Calculate a 90% confidence interval for n = 49, ¯ x = 28, σ = 28

Solution:

A confidence interval is a range of numbers that contains a population parameter.

C = 90% = 0.9

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

The z score of α/2 is the same as the z score 0.45 (0.5 - 0.05) which is equal to 1.65. Hence, the margin of error E is:

[tex]E=z_\frac{\alpha}{2}*\frac{\sigma}{\sqrt{n} } =1.65*\frac{28}{\sqrt{49} } =6.6[/tex]

The confidence interval = [tex]\bar x \pm E=28 \pm 6.6 = (21.4,\ 34.6)[/tex]

The 90% confidence is between 21.4 and 34.6.

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