SOLUTION: Although male polar bears weigh only about one pound at birth, the mean weight of a random sample of 10 adult male polar bears is 1200 pounds with a standard deviation of 100 pound

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Question 868431: Although male polar bears weigh only about one pound at birth, the mean weight of a random sample of 10 adult male polar bears is 1200 pounds with a standard deviation of 100 pounds. Construct and interpret a 98% confidence interval for the mean weight of all adult male polar bears. Assume that the population is evenly distributed.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use a table to find that the critical value is t=2.821. The degrees of freedom are df+=+n-1+=+10-1+=+9. Look in the row that starts with 9 and look above the 98%. The value you'll see in this spot is 2.821


So we're given


xbar = 1200 (sample mean)
t = 2.821 (see above)
s = 100 (sample standard deviation)
n = 10 (sample size)


Now compute the lower bound (L) and the upper bound (U) of the confidence interval.


Lower Bound:

L = xbar - t*s/sqrt(n)
L = 1200 - 2.821*100/sqrt(10)
L = 1,110.79214720666


Upper Bound:

U = xbar + t*s/sqrt(n)
U = 1200 + 2.821*100/sqrt(10)
U = 1,289.20785279334


The 98% confidence interval is approximately (1110.79214720666, 1289.20785279334)


So if we construct 100 confidence intervals, then about 98 of them will contain the true population mean.