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The randomly selected delivery times (in minutes) of two fast food restaurants are as follows. This table displays the randomly selected delivery times (in minutes) for two fast food restaurants. Fast Food 1 Fast Food 2 42 40 38 37 37 40 39 41 38 38 40 46 45 41 41 37 40 40 Which of the following statements is false? (1 point) Responses Both fast food restaurants have the same median delivery time of 40 minutes. Both fast food restaurants have the same median delivery time of 40 minutes. Both fast food restaurants have exactly one modal delivery time of 40 minutes. Both fast food restaurants have exactly one modal delivery time of 40 minutes. Neither data set contains an outlier. Neither data set contains an outlier. Both fast food restaurants have the same mean delivery time of 40 minutes.

1 answer

To determine which statement is false, we need to analyze the delivery times for both fast food restaurants.

Fast Food 1 Delivery Times: 42, 38, 37, 39, 38, 40, 40
Sorted Fast Food 1: 37, 38, 38, 39, 40, 40, 42

Fast Food 2 Delivery Times: 40, 37, 41, 46, 45, 41, 37, 40
Sorted Fast Food 2: 37, 37, 40, 40, 41, 41, 45, 46

Calculate:

  1. Medians:

    • Fast Food 1: (39 + 40)/2 = 39.5 (the middle two numbers are 39 and 40)
    • Fast Food 2: (40 + 41)/2 = 40.5 (the middle two numbers are 40 and 41)

  2. Modes:

    • Fast Food 1: Mode is 40 (appears twice).
    • Fast Food 2: Mode is 40 (also appears twice).

  3. Outliers:

    • Fast Food 1: No outliers (all values within 1.5 * IQR)
    • Fast Food 2: No outliers (all values within 1.5 * IQR)

  4. Means:

    • Fast Food 1: (42 + 38 + 37 + 39 + 38 + 40 + 40) / 7 = 39.7143
    • Fast Food 2: (40 + 37 + 41 + 46 + 45 + 41 + 37 + 40) / 8 = 41

Statements check:

  1. Both fast food restaurants have the same median delivery time of 40 minutes.

    • False (Fast Food 1 median = 39.5, Fast Food 2 median = 40.5)

  2. Both fast food restaurants have exactly one modal delivery time of 40 minutes.

    • True (Both have mode 40).

  3. Neither data set contains an outlier.

    • True (No outliers in either dataset).

  4. Both fast food restaurants have the same mean delivery time of 40 minutes.

    • False (Fast Food 1 mean ≈ 39.71, Fast Food 2 mean = 41).

The false statements are about the median being the same and about the mean being the same. However, since you requested to identify specifically one statement as false, the first statement about the median is the most direct claim about equality, which is incorrect.

Final Answer:

Both fast food restaurants have the same median delivery time of 40 minutes. (This statement is false.)