Question

Im struggling! WILL MEDAL
Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume
that the population has a normal distribution.
n = 10, x = 12.3, s = 3.9, 95% confidence

9.55 < µ < 15.05
9.52 < µ < 15.08
9.51 < µ < 15.09
10.04 < µ < 14.56

Answer 1

What does 's' represent ?

Answer 2

i believe that it must mean ST. DEV

Answer 3

Ok, then !
Give me a few moments I'm a little rusty on this =)

Answer 4

Thank you! I am so grateful! =)

Answer 5

95% confidence means that 95% of values are within 2 standard deviations of the mean (see attached)
A confidence interval for \(\mu\) is given by : \[x \pm 2\sigma _{x}\]\[12.3 \pm 2 \sqrt{\frac{ 3.9 }{ 10 }}\]
Reference: http://www.kean.edu/~fosborne/bstat/06amean.html

Answer 6

11.051 - 13.549 is what i got. do i subtract 2 form either side?

Answer 7

You got that how ?

Answer 8

\[12.3 \pm 2 \sqrt{\frac{ 3.9 }{ 10 }}\] Translates to : \[12.3 - 2 \sqrt{\frac{ 3.9 }{ 10 }} <\mu<12.3 + 2 \sqrt{\frac{ 3.9 }{ 10 }}\]

Answer 9

by computing the last calculation 12.3+2sqrt3.9/10

Answer 10

Little mistake there, since s is the standard deviation, there's no need for the square root on \(\sigma\). Hence \[12.3 - 2 \frac{ 3.9 }{\sqrt{ 10 }} <\mu<12.3 + 2 \frac{ 3.9 }{\sqrt{ 10 }}\]