Chapter 7—Introduction to Sampling Distributions
When applicable, selected problems in each section will be done following the appropriate stepby-step procedures outlined in the corresponding sections of the chapter. Other problems will provide key points and the answers to the questions, but all answers can be arrived at using the appropriate steps.

Section 7-1 Exercises
7.1. Step 1: The population mean of 125 is given Step 2: Compute the sample mean using Equation 7-3 x = (103 + 123 + 99 + 107 + 121 + 100 + 100 + 99)/8 = 852/8 = 106.5 Step 3: Compute the sampling error using Equation 7-1 Sampling Error = x - µ = 106.5 – 125 = -18.50 The sample of eight has a sampling error of -18.50. The sample has a smaller mean than the population as a whole. 7.3. The following steps can be used to determine the sampling error: Step 1: Determine the population mean. The population mean is computed as follows: x 273 µ=∑ = = 11.38 N 24 Step 2: Compute the sample mean. ∑ x = 61 = 10.17 x= n 6 Step 3: Compute the sampling error. Sampling error = x − µ = 10.17 − 11.38 = −1.21 7.5. a. Step 1: Compute the population mean using Equation 7-2. µ= 10+14+32+9+34+19+31+24+33+11+14+30+6+27+33+32+28+30+ 10+31+19+13+6+35)/24 = 531/24 = 22.125 Step 2: Compute the sample mean using Equation 7-3 x = (32+19+6+11+10+19+28+9+13+33)/10 = 180/10 = 18 Step 3: Compute the sampling error using Equation 7-1 Sampling Error = x - µ = 18 – 22.125 = -4.125 The sample of ten has a sampling error of -4.125. The sample has a smaller mean than the population as a whole. For parts (b) and (c), the population rank order is shown below.
6 14 31 6 19 31 9 19 32 10 24 32 10 27 33 11 28 33 13 30 34 14 30 35

b. In order to calculate the extreme sampling error, the data needs to be rank-ordered from lowest to highest. Use the rank-order table shown above. Calculate the sample mean for the 6 smallest values and