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A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for μ is _____. a. 6.000 to 14.000 b. 8.384 to 11.616 c. 8.462 to 11.538 d. 9.846 to 10.154

Sagot :

ogorwyne

Answer:

B.  8.384 to 11.616

Step-by-step explanation:

We have

mean = 10

s = 4

n =  26

the degrees of freedom = n-1

= 26 - 1 = 25

α = 1-95%

= 1 - 0.95

= 0.05

α/2 = 0.05/2 = 0.025

using the t table

t0.025, 25 = 2.06

we find the margin of error

t * s/√n

= 2.06 * 4/√26

= 1.616

10-1.616 < μ < 10+1.616

= 8.384<μ<11.616

therefore option b is the right solution

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