4. Assume that you will take a sample of size 36 from a population of GPAs with a mean value of 2.1 and a population standard deviation of 0.4.
a. Specify the sampling distribution of X ¯, your sample mean value.
b. Calculate P[X ¯>2.20].
5. Suppose that you do know the value of the population standard deviation and that you want to calculate an 80% CI for μ, the population mean value. Determine the value of the critical number that you would use to calculate this CI.
6. Given the following probability distribution table for the random variable X:
X: -3 2 7
f(x): 0.3 0.5 0.2
a. Calculate the Expected Value of X.
b. Calculate the Variance of X.
7. Given the following heights measured in inches: 68, 72, 65, 69, 72:
a. Calculate the mean height for this sample.
b. Calculate the standard deviation for this sample of heights.
8. Suppose that you will pick two cards from a standard deck of 52 cards, without replacement, and you are only interested in whether each of the cards that you select is a diamond, or not.
a. Draw the complete tree diagram, with all of the twig probabilities in place.
b. What is the probability that exactly 1 of the two cards that you select is a diamond?
9. Use the data set in question 7 to find the 95% CI for μ.
10. Name the two desirable properties for any CI.
11. Students were given a quiz, and the amount of time (measured in minutes) it took each student to finish the quiz was recorded. The results follow:
10, 11, 11.25, 12.5, 12.5, 14, 15, 18, 18, 20, 22
a. Complete the 5-Number summary of this data set:
Min: _____
Q1: _____
Q2: _____
Q3: _____
Max: _____
b. Calculate the IQR for this data set.
c. Calculate the Upper Fence for this data set.
d. What is the reason that you would calculate the Fences in an analysis?
12. Consider the following scatterplots:
a. Which scatterplot has the smallest r-value?
b. Which scatterplot shows the weakest linear correlation?
c. Which scatterplot has an r-value closest to 1?