# Degrees of Freedom

1. The following data CELLPHONE represent the digital-mode talk time in hours and the battery capacity in milliampere-hours of cell phones.

Name Type Price Talk Time Battery Capacity

Samsung SPH-N200 CDMA 200 4.5 800

Nokia 6185 CDMA 99 4 1500

Sanyo SCP-4500 CDMA 180 3 1300

Kyocera Smart Phone QCP-6035 CDMA 450 2 1550

Nokia 5180 CDMA 20 2.75 900

LG TM510 CDMA 130 1.75 875

Audiovox CDM 9100 CDMA 100 1.75 750

Motorola V120c CDMA 100 2.25 1100

Kyocera QCP 2035a CDMA 100 1.75 850

Motorola V60c CDMA 400 1.5 450

Motorola Timeport O8767 CDMA 150 2.25 900

Nokia 7160 TDMA 130 2.25 900

Nokia 8260 TDMA 200 3.25 900

Motorola V2397 TDMA 50 2.25 700

Ericsson R278d TDMA 100 2.25 800

Ericsson R280LX TDMA 195 2.5 800

Nokia 6160 TDMA 140 2.25 900

Nokia 5160 TDMA 140 2 900

a. Compute the coefficient of correlation r.

b. What conclusions can you reach about the relationship between the battery capacity and the digital-mode talk time?

c. You would expect the cell phones with higher battery capacity to have a higher talk time. Is this borne out by the data?

2. For fast food restaurants, the drive-through window is an increasing source of revenue. The chain that offers the fastest service is considered most likely to attract additional customers. In a study of drive-through times (from menu board t departure) at fast-food chains, the average time was 150 seconds for Wendy's, 167 seconds for McDonald's, 169 seconds for Checkers, 171 seconds for Burger King, and 172 seconds for Long John Silver's. Suppose the study was based on 20 customers for each fast-food chain and the following ANOVA table was developed.

SOURCE Degrees of Freedom Sum of squares Mean squares F

Among chains 4 6,536 1,634.0 12.51

Within chains 95 12,407 130.6

a. At the 0.05 level of significance, is there evidence of a difference in the average drive-through times of the five chains?

b. If appropriate, determine which fast-food chains differ in drive through times.

c. What conclusions can you reach about which fast-food chains have the best drive-through times?

#### Solution Summary

1. The following data CELLPHONE represent the digital-mode talk time in hours and the battery capacity in milliampere-hours of cell phones.

Name Type Price Talk Time Battery Capacity

Samsung SPH-N200 CDMA 200 4.5 800

Nokia 6185 CDMA 99 4 1500

Sanyo SCP-4500 CDMA 180 3 1300

Kyocera Smart Phone QCP-6035 CDMA 450 2 1550

Nokia 5180 CDMA 20 2.75 900

LG TM510 CDMA 130 1.75 875

Audiovox CDM 9100 CDMA 100 1.75 750

Motorola V120c CDMA 100 2.25 1100

Kyocera QCP 2035a CDMA 100 1.75 850

Motorola V60c CDMA 400 1.5 450

Motorola Timeport O8767 CDMA 150 2.25 900

Nokia 7160 TDMA 130 2.25 900

Nokia 8260 TDMA 200 3.25 900

Motorola V2397 TDMA 50 2.25 700

Ericsson R278d TDMA 100 2.25 800

Ericsson R280LX TDMA 195 2.5 800

Nokia 6160 TDMA 140 2.25 900

Nokia 5160 TDMA 140 2 900

a. Compute the coefficient of correlation r.

b. What conclusions can you reach about the relationship between the battery capacity and the digital-mode talk time?

c. You would expect the cell phones with higher battery capacity to have a higher talk time. Is this borne out by the data?

2. For fast food restaurants, the drive-through window is an increasing source of revenue. The chain that offers the fastest service is considered most likely to attract additional customers. In a study of drive-through times (from menu board t departure) at fast-food chains, the average time was 150 seconds for Wendy's, 167 seconds for McDonald's, 169 seconds for Checkers, 171 seconds for Burger King, and 172 seconds for Long John Silver's. Suppose the study was based on 20 customers for each fast-food chain and the following ANOVA table was developed.

SOURCE Degrees of Freedom Sum of squares Mean squares F

Among chains 4 6,536 1,634.0 12.51

Within chains 95 12,407 130.6

a. At the 0.05 level of significance, is there evidence of a difference in the average drive-through times of the five chains?

b. If appropriate, determine which fast-food chains differ in drive through times.

c. What conclusions can you reach about which fast-food chains have the best drive-through times?