Question

Ok, let’s say there’s about 10 calories per ounce of human blood and let’s assume that vampires have the same daily caloric need as humans: 2,000 calories per day. This would mean that vampires would need about 200 ounces, or 12.50 pints, of human blood per day. This would require the vampire to fully exsanguinate about on 1.5 adult humans per day (night?)!

Luckily for us mortals, it turns out that vampires need less than 2,000 calories per day (they have slow metabolisms; they’re dead after all). Indeed, Dr. Von Hellsong surveyed the entire population of vampires and found that they intake an average of 666 calories 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 vampires each. One sample (i.e., the sample of interest) has a mean daily caloric intake of 659 calories, with a standard deviation of 13.33 calories.

Given the above information, answer the following questions:

1.What is the standard error of the mean of the sampling distribution of means (round to two decimal places)?

2. What is the z-score of the sample of interest ?

3. What is the probability that a sample of 25 vampires will be drawn from the population with a mean daily calorie intake less than our sample of interest (give me all four decimals)?

4. What is the probability that a sample of 25 vampires will be drawn from the population with a mean daily calorie intake greater than our sample of interest (give me all four decimals)?

5. What is the probability that a sample of 25 vampires 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 decimals)?

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 .

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.

Answer 1

1)

The standard error of the mean of sampling distribution of means =

Standard error of the actual population / sqrt(sample size)

=18.97/sqrt(25)

=3.794

2)

The z-score of the sample of interest is given by :

(659 – true pop mean )/ standard error of the mean of sampling distribution of means

=(659-666)/3.794

=-1.845

3)

Let X denote the random variable of mean of the samples.

And Z denote the standard normal distribution.

Probability (X<659)=P(Z<-1.845)

=(-1.845)

=0.0325

4)

This probability is 1 minus the probability obtained in 3)

=1-0.0325

=0.9675