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. Unwilling 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 sigma = 60 kg, and he has data from a simple random sample of n = 6 polar bears from Greenland. Their masses, in kg, are 320, 350, 300, 475, 380, 425 The sample mean polar bear mass is bar x = 375 kg. First, determine if the requirements for a z-confidence interval are met. 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 not met because there is an outlier in the sample, indicating that polar o 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 with a known population standard deviation.

Answer 1

The requirements for a z-confidence interval are met because the sample is a simple random sample from a normal distribution with a known population standard deviation.

Explanation:

The requirements for a z-confidence interval are met because the sample is a simple random sample from a normal distribution with a known population standard deviation.

However, since the sample is small, we should use the Student's t-distribution with 5 degrees of freedom (sample size-1) instead of the Normal distribution.

The t-distribution is the right choice when the data distribution is approximately normal and the sample size is less than 30.

The t-confidence interval will depend on the level of confidence desired.