Question 1201637: In a survey, 11 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $43 and standard deviation of $15. Construct a confidence interval at a 95% confidence level.
Give your answers to one decimal place.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! sample size is 11.
sample mean is 43 dollars.
standard deviation is 15 dollars.
because you are looking for the mean of a sample of specified size, use the standard error rather than the standard deviation.
standard error = standard deviation divided by square root of sample size = 15 / sqrt(11) = 4.522670169.
at 95% two tailed confidence level, the critical t-score with 10 degrees of freedom is equal to plus or minus 2.228138842.
use the t-score formula to find the equivalent raw score.
on the high side, t = (x - m) / s becomes 2.228138842 = (x - 43) / 4.522670169.
solve for x to get x = 2.228138842 * 4.522670169 + 43 = 53.07713707.
on the low side, t = (x - m) / s becomes -2.228138842 = (x - 43) / 4.522670169.
solve for x to get x = -2.228138842 * 4.522670169 + 43 = 32.92286293.
your 95% confidence interval is from 32.92286293 to 53.07713707.
in the t-score formula for this problem, .....
t is the critical t-score
x is the critical raw score
m is the mean
s is the standrd error.
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