Question

Suppose that Drake works for a research institute in Greenland and is given the job of treating wild polar bears there for hypothyroidism using medicated darts. The appropriate dosage depends on the bear's mass. Eager to head into the wilderness, he prints out the statistics he needs and sets off, planning to prepare the darts along the way Two days into his trek, however, Drake spills a cup of coffee on the printout. Unwiling to admit to his boss what happened, he decides to estimate the polar bear mass with the information he has remaining. He knows the population standard deviation to be ơ-60kg, and he has data from a simple random sample of n-10 polar bears from Greenland. Their masses, in kg, are 275,250, 325,310,240, 360, 350, 400, 380, 400 The sample mean polar bear mass isx 329kg. If you wish, you may download the data in your preferred format. Crunchlt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc First, determine if the requirements for a z-confidence interval are met. The requirements are not met because there is an outlier in the sample, indicating that polar bear masses do not come from a normal distribution or that the sample was not a simple random sample. The requirements are met because the sample is a simple random sample from a normal distribution and the standard deviation can be estimated from the sample. The requirements are not met because the population standard deviation is not known. The requirements are met because the sample is a simple random sample from a normal distribution with a known population standard deviation. Next, calculate the lower and upper limits bounds) for a 99% confidence interval for the mean polar bear mass in Greenland. Give your answer precise to one decimal place. kg lower limit: Next, calculate the lower and upper limits (bounds) for a 99% confidence interval for the mean polar bear mass in Greenland. Give your answer precise to one decimal place. kg lower limit kg upper limit Finally, summarize the results. O There is 99% confidence that the polar bear mass sample mean is between the lower and upper limits of the O There is a 99% chance that the Greenland polar bear mass population mean is between the lower and upper limits of O There is a 99% chance that a randomly selected polar bear in Greenland will have a mass between the lower and O There is 99% confidence that the lower and upper limits of the confidence interval contains the Greenland polar confidence interval. the confidence interval. upper limits of the confidence interval. Iear s pican.

Answer 1

If the requirement for a z-confidence interval are met:

Answer: The requirements are met because the sample is a simple random sample from a normal distribution with a known population standard deviation.

x̅ =   329, σ =   60, n =   10
α = 1-0.99 = 0.01

99% Confidence interval :              

At α = 0.01, two tailed critical value, z crit = NORM.S.INV(0.01/2) = 2.576
                  
Lower limit = x̅-z-crit*σ/√n = 280.1      
Upper limit = x̅+z-crit*σ/√n = 377.9

Summarize:

There is 99% chance that the Greenland polar bear mass population mean is between the lower and upper limit of the confidence interval.