Stats help please! 3?

Question

Bill claims that the mean weight of the population of bears

living in Yellowstone National Park is 200 pounds. A sample of 54

bears from Yellowstone has a mean weight of 182.9 pounds. Does the

claim hold at the 0.01 significance level? Assume that

sigma=121.8. How does this question relate to the previous bear question relate to finding a

99% confidence interval for the mean weight of the population of

bears in Yellowstone using that same sample of 54 bears.

That is:

How are the two bear questions related to one another?

Can we deduce the answer of one from the answer of another?

If so, which, why, and how?

If not, why not?

Answer 1

Confidence intervals are used to find a region in which we are 100 * ( 1 - α )% confident the true value of the parameter is in the interval.

For large sample confidence intervals about the mean you have:

xBar ± z * sx / sqrt(n)

where xBar is the sample mean

z is the zscore for having α% of the data in the tails, i.e., P( |Z| > z) = α

sx is the sample standard deviation

n is the sample size

The sample mean xbar = 182.9

The sample standard deviation sx = 121.8

The sample size n = 54

The z score for a 0.99 confidence interval is the z score such that 0.005 is in each tail.

z = 2.575829

The confidence interval is:

( xbar - z * sx / sqrt( n ) , xbar + z * sx / sqrt( n ) )

( 140.2059 , 225.5941 )

this goes with the question about with the hypothesis test.  note that the CI contains the value of 200 and the hypothesis test said 200 was a plausible value as well.