### Essay Writes

Question 1

Using the telephone numbers listedin your local directory as your population, randomly obtain 20 samples of size3. From each telephone number identified as a source, take the fourth, fifth,and sixth digits.

• Calculate the mean of the 20 samples

• Draw a histogram showing the 20sample means. (Use classes -0.5 to 0.5, 0.5 to 1.5, 1.5 to 2.5 and so on).

• Describe the distribution of thex-bars that you see in part b (shape of distribution, center, and the amount ofdispersion).

• Draw 20 more samples and add the 20new x-bars to the histogram in part b. Describe the distribution that seems tobe developing.

Use the empirical rule to test fornormality. See the sampling distribution of sample means and the central limittheorem develop from your own data!

Question 2

Consider a population with μ = 43and σ = 5.2.

• Calculate the z-score for an x̅ of 46.5 from a sample of size 35.

• Could this z-score be used incalculating probabilities using Table 3 in Appendix B? Why or why not?

Question 3

State the null and alternativehypotheses for each of the following:

• You want to show an increase inbuying and selling of single-family homes this year when compared with lastyear’s rate.

• You are testing a new recipe for“low-fat” cheesecake and expect to find that its taste is not as good astraditional cheesecake.

• You are trying to show that musiclessons have a positive effect on a child’s self-esteem.

• You are investigating therelationship between a person’s gender and the automobile he or she drives—specificallyyou want to show that more males than females drive truck-type vehicles.

Maximum Points

Meets or exceeds establishedassignment criteria

40

Demonstrates an understanding oflesson concepts

20

Clearly present well-reasonedideas and concepts

30

Mechanics, punctuation, sentencestructure, spelling that affects clarity, and citation of sources asneeded

10

Total

100