Question

In: Statistics and Probability

An iceberg consists of frozen freshwater that has broken away from a glacier, and could be...

An iceberg consists of frozen freshwater that has broken away from a glacier, and could be more than 15,000 years old. Icebergs in the Grand Banks area are estimated to weigh between 100,000 and 200,000 tons. Suppose a team of scientists aboard a research vessel operating in the Grand Banks area selects a random sample of 49 icebergs. The height is carefully measured for each, and the sample mean is x = 101 meters. Assume σ = 25 meters.

(a) Find a 99% confidence interval for the mean height of icebergs in the Grand Banks area (in meters). (Round your answers to four decimal places.)

(____________ , __________)meters

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 101

Population standard deviation = = 25

Sample size = n =49

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 2.576 * ( 25/ $\sqrt$ 49)

= 9.2000

At 99% confidence interval estimate of the population mean is,

- E < < + E

101 - 9.2000< < 101 +9.2000

91.8000< < 110.2000

(91.8000 , 110.2000)

orchestra answered 1 year ago

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