Let’s simulate the sampling distribution related to the disc jockey’s concern for “length of cut” in Exercise 7.62.

a. Use a computer to randomly generate 50 samples, each of size 10, from a normal distribution with mean 135 and standard deviation 10.

Find the “sample total” and the sample mean for each sample.

b. Using the 50 sample means, construct a histogram and find their mean and standard deviation.

c. Using the 50 sample “totals,” construct a histogram and find their mean and standard deviation.

d. Compare the results obtained in parts b and c.

Explain any similarities and any differences observed.

MINITAB (Release 14)

a. Use the Normal RANDOM DATA commands on page 327, replacing generate with 50, store in with C1–C10, mean with 135, and standard deviation with 10. Use the ROW STATISTICS commands on page 368, selecting Sum and replacing input variables with C1–C10 and store result in with C11. Use the ROW STATISTICS commands, again selecting Mean and then replacing input variables with C1–C10 and store result in with C12.

b. Use the HISTOGRAM commands on page 61 for the data in C12. To adjust the histogram, select Binning with midpoint. Use the MEAN and STANDARD DEVIATION commands on pages 74 and 88 for the data in C12.

c. Use the HISTOGRAM commands on page 61 for the data in C11. To adjust the histogram, select Binning with midpoints. Use the MEAN and STANDARD DEVIATION commands on pages 74 and 88 for the data in C11.

d. Use the DISPLAY DESCRIPTIVE STATISTICS commands on page 98 for the data in C11 and C12.

Excel

a. Use the Normal RANDOM NUMBER GENERATION commands on page 328, replacing number of variables with 10, number of random numbers with 50, mean with 135, and standard deviation with 10.

Activate cell K1.

Choose: Insert function, fx  All  SUM  OK Enter: Number1: (A1:J1 or select cells)

Drag: Bottom right corner of sum value box down to give other sums Activate cell L1. Use the AVERAGE INSERT FUNCTION commands in Exercise 7.13b on page 368, replacing Number1 with A1:J1.

b. Use the RANDOM NUMBER GENERATION Patterned Distribution commands in Exercise 6.66 on page 336, replacing the first value with 125.4, the last value with 144.6, the steps with 3.2, and the output range with M1. Use the HISTOGRAM commands on page 61 with column L as the input range and column M as the bin range. Use the MEAN and STANDARD DEVIATION commands on pages 74 and 88 for the data in column L.

c. Use the RANDOM NUMBER GENERATION Patterned Distribution commands in Exercise 6.66 on page 336, replacing the first value with 1254, the last value with 1446, the steps with 32, and the output range with M20. Use the HISTOGRAM commands on page 61 with column L as the input range and cells M20–? as the bin range. Use the MEAN and STANDARD DEVIATION commands on pages 74 and 88 for the data in column K.

d. Use the DESCRIPTIVE STATISTICS commands on page 98 for the data in columns K and L.