Question

Did you know that leprechauns LOVE Guinness Stout? In fact, leprechauns do not have to consume anything else to survive; they simply get all of their calories from Guinness Stout. If a standard, 12-ounce Guinness bottle has only 125 calories, then a leprechaun would need to consume 16 bottles of Guinness per day, assuming that they have the same daily caloric need as humans (i.e., 2,000 calories per day)!

However, leprechauns actually need more than 2,000 calories per day. Indeed, Dr. McPatrick surveyed the entire population of leprechauns and found that they intake an average of 2,805 calories (or 22.4 Guinness bottles) per day, with a standard deviation of 18.97 calories.

For this assignment, we are going to create a sampling distribution of means using an infinite number of samples containing 25 leprechauns each. One sample (i.e., the sample of interest) has a mean daily caloric intake of 2,798 calories, with a standard deviation of 13.33 calories.

5) What is the probability that a sample of 25 leprechauns will be drawn from the population with a mean daily calorie intake between our sample of interest and the population mean (give me all four decimal places; 2.5 pts)?

6) With a criterion of p= .05, what is the two-tailed critical values that define the regions of rejection? Does the mean of the sample of interest fall within a region of rejection? What does this tell us in terms of the sample’s representativeness of the population? Explain your answers (1.25 pt per question; 3.75 pts total).

7) With a criterion of p= .05, what is the one-tailed critical value that defines the region of rejection if we are only interested in whether or not the target sample’s mean is too far below the population mean to be representative of the population? Does the mean of the sample of interest fall within the region of rejection? What does this tell us in terms of the sample’s representativeness of the population? Explain your answers (1.25 pt per question; 3.75 pts total)

Answer 1