Using the telephone numbers listed in your local directory as your population, randomly obtain 20 samples of size 3. From each telephone number identified as a source, take the fourth, fifth, and sixth digits.
Using the telephone numbers listed in your local directory as your population, randomly obtain 20 samples of size 3. From each telephone number identified as a source, take the fourth, fifth, and sixth digits.
a. Calculate the mean of the 20 samples
b. Draw a histogram showing the 20 sample means. (Use classes -0.5 to 0.5, 0.5 to 1.5, 1.5 to 2.5 and so on).
c. Describe the distribution of the x-bars that you see in part b (shape of distribution, center, and the amount of dispersion).
d. Draw 20 more samples and add the 20 new x-bars to the histogram in part b. Describe the distribution that seems to be developing
Use the empirical rule to test for normality. See the sampling distribution of sample means and the central limit theorem develop from your own data!
Question 2
Consider a population with ì = 43 and ó = 5.2.
a. Calculate the z-score for anx̅ of 46.5 from a sample of size 35.
b. Could this z-score be used in calculating probabilities using Table 3 in Appendix B? Why or why not?
Question 3
State the null and alternative hypotheses for each of the following:
a. You want to show an increase in buying and selling of single-family homes this year when compared with last year’s rate.
b. You are testing a new recipe for “low-fat” cheesecake and expect to find that its taste is not as good as traditional cheesecake.
c. You are trying to show that music lessons have a positive effect on a child’s self-esteem.
d. You are investigating the relationship between a person’s gender and the automobile he or she drives—specifically you want to show that more males than females drive truck-type vehicles
Describe the district ution of the x-bars that you see in part b (shape of distribution, center, and the amount of depersion).
To randomly obtain 20 samples of size 3 from the telephone numbers listed in your local directory, you can follow these steps:
1. Obtain a local directory: Get hold of a copy of the local telephone directory that contains a list of phone numbers in your area.
2. Determine the population: Consider all the telephone numbers listed in the directory as your population. This will be the total set of telephone numbers you can choose from.
3. Randomly select samples: To obtain 20 random samples of size 3, you need to randomly select three digits from each telephone number identified as a source.
a. Start by assigning a number to each entry in the telephone directory. For example, you can number them from 1 to N, where N is the total number of entries in the directory.
b. Use a random number generator: Utilize a random number generator (RNG) to generate 20 unique random numbers within the range of 1 to N. These numbers will represent the entries in the directory that you will select as your sources.
c. Select the telephone numbers: Take the corresponding telephone numbers from the randomly generated numbers. These telephone numbers will serve as your sources for each sample.
d. Obtain the digits: From each source telephone number, extract the fourth (x), fifth (y), and sixth (z) digits. These three digits will represent one sample.
e. Repeat steps b-d, until you have obtained 20 samples in total.
By following these steps, you will be able to randomly select 20 samples of size 3 from the telephone numbers listed in your local directory.