Question 1193737: In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1=not attractive; 10=extremely attractive). Construct a confidence interval using a 99% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females?
8, 7, 2, 8, 6, 6, 7, 8, 7, 9, 3, 8
Answer by math_tutor2020(3817)   (Show Source):
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There are n = 12 items in this sample.
Use your calculator to compute the mean and sample standard deviation of the given data values
xbar = 6.58333 = sample mean
s = 2.10878 = sample standard deviation
both of which are approximate
Use a table like this one
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
to look at the bottom row marked in blue (it starts with Z)
The value 2.576 is just above the 99% confidence level.
The z critical value is roughly z = 2.576 when we have 99% confidence level.
E = margin of error
E = z*s/sqrt(n)
E = 2.576*2.10878/sqrt(12)
E = 1.56815
which is approximate.
L = lower bound of the confidence interval
L = xbar - E
L = 6.58333 - 1.56815
L = 5.01518
L = 5.02
U = upper bound of the confidence interval
U = xbar + E
U = 6.58333 + 1.56815
U = 8.15148
U = 8.15
The 99% confidence interval is approximately (5.02, 8.15) when presented in the template of (L, U)
This is equivalent to 5.02 < mu < 8.15 when written in the form L < mu < U
We're 99% confident the true population mean attractiveness rating is somewhere between a rating of 5.02 and 8.15
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