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    Degrees of Freedom

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    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?

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    https://brainmass.com/statistics/degrees-of-freedom/degrees-of-freedom-17209

    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?

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