Sampling Distributions Supplementary Problems for Beginning Statistics
Review the following concepts if necessary:
- Simple Random Sampling for Beginning Statistics
- Sampling Distributions for Beginning Statistics
- Mean and Standard Deviation of the Sample Mean for Beginning Statistics
- Shape of the Sampling Distribution of the Sample Mean and the Central Limit Theorem for Beginning Statistics
- Sampling Distribution of the Sample Proportion for Beginning Statistics
- Shape of the Sampling Distribution of the Sample Proportion and the Central Limit Theorem for Beginning Statistics
Simple Random Sampling
- Rather than have all 25 students in her Statistics class complete a teacher evaluation form, Mrs. Jones decides to randomly select three students and have the department chairman interview the three concerning her teaching after the course grade has been given. How many different samples of size 3 can be selected?
- USA Today lists the 1900 most active New York stock exchange issues. How many samples of size three are possible when selected from these 1900 stock issues?
Using Random Number Tables
- In a table of random numbers such as Table 7.1, what relative frequency would you expect for each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9?
- The 100 U.S. Senators are listed in alphabetical order and then numbered as 00, 01, . . . , 99. Use Table 7.1 to select 10 of the senators. Start with the two digits in columns 31 and 32 and row 6. The first selected senator is numbered 76. Reading down the two columns from the number 76, what are the other 9 two-digit numbers of the other selected senators?
Ans. 59, 78, 44, 93, 69, 25, 43, 50, and 45
Using the Computer to Obtain a Simple Random Sample
- Use EXCEL to select 25 of the 1900 stock issues discussed in Problem 7.28. Give the numbers in ascending order of the 25 selected stock issues. Assume the stock issues are numbered from 1 to 1900.
- Use MINITAB to select 50 of the 3143 counties in the United States. Give the numbers in ascending order of the 50 selected counties. Assume counties are in alphabetical order and are numbered from 1 to 3143.
Ans: ' The formula, =INT(RAND()*1900)+1, is entered into any Excel cell and a click-and-drag is performed from A1:A25. With the cells still selected, copy the values to A1:A25 using Copy Paste Special Values. Now press the button to arrange them into ascending order. The twenty five numbers, rearranged into five columns, are given below. Your results will vary because the formula is volatile. Note that repetition could occur.
Ans. MINITAB can be used to select the random sample of counties. The pull down Calc Random Data Integer is used. The Integer Distribution dialog box is filled as follows: Generate 50 rows of data, store in column C1, Minimum value = 1 and maximum value = 3134. The following 50 numbers are obtained when column C1 is printed out (rearranged).
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