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:

What is the standard error of the mean of the sampling distribution of means? 18.97/sqrt25=3.79

What is the z-score of the sample of interest? 659-666/3.79=-1.85

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)?(X<659)=P(Z<-1.85) =0.0325

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? 1-0.0325=0.9675

1. 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?

2. 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

3. 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.
P(659 < X < 666)
= 0.5 - P(X < 659)
= 0.5 - 0.0325
= 0.4675

#2.
For significance level of 0.05, critical values of rejection region are +/- 1.96
If the value of test statistics fall beyond this value i.e. less than -1.96 or greater than 1.96, we reject the null hypothesis.

#3.
For significance level of 0.05, critical values of rejection region are +/- 1.645
Yes, sample of interest, z-value is less than -1.645 i.e. in the rejection region.
Reject the null hypothesis.
This means the mean of the sample is less than the population mean.