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

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.

Neither data set contains an outlier.
Neither data set contains an outlier.

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.
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1 answer

To determine which statement is false, let's analyze the delivery times for both fast food restaurants:

Delivery Times

Fast Food 1: 42, 38, 37, 39, 38, 40, 45, 41, 40
Fast Food 2: 40, 37, 40, 41, 38, 46, 41, 40, 40

1. Calculate the Mean Delivery Time

Fast Food 1: \[ \text{Mean} = \frac{42 + 38 + 37 + 39 + 38 + 40 + 45 + 41 + 40}{9} = \frac{360}{9} = 40 \]
Fast Food 2: \[ \text{Mean} = \frac{40 + 37 + 40 + 41 + 38 + 46 + 41 + 40 + 40}{9} = \frac{364}{9} \approx 40.44 \]

So, Fast Food 1 has a mean of 40 minutes and Fast Food 2 has a mean of approximately 40.44 minutes. Therefore, the first statement is false.

2. Calculate the Median Delivery Time

Fast Food 1: The sorted delivery times are: 37, 38, 38, 39, 40, 40, 41, 42, 45. The median (5th value) is 40.
Fast Food 2: The sorted delivery times are: 37, 38, 40, 40, 40, 40, 41, 41, 46. The median (5th value) is also 40.

Both restaurants have the same median delivery time of 40 minutes, so the second statement is true.

3. Check for Outliers

Fast Food 1: Using the IQR method:
- Lower quartile (Q1) = 38, upper quartile (Q3) = 41.
- IQR = Q3 - Q1 = 41 - 38 = 3.
- Determine boundaries:
  - Lower boundary = Q1 - 1.5*IQR = 38 - 4.5 = 33.5
  - Upper boundary = Q3 + 1.5*IQR = 41 + 4.5 = 45.5
All observations are within this range, so no outliers.
Fast Food 2: Using the IQR method:
- Lower quartile (Q1) = 40, upper quartile (Q3) = 41.
- IQR = Q3 - Q1 = 41 - 40 = 1.
- Determine boundaries:
  - Lower boundary = Q1 - 1.5*IQR = 40 - 1.5= 38.5
  - Upper boundary = Q3 + 1.5*IQR = 41 + 1.5 = 42.5
All observations are within this range, so no outliers.

Both data sets contain no outliers, so the third statement is true.

4. Find the Mode Delivery Time

Fast Food 1: Delivery times: 42 (1), 38 (2), 37 (1), 39 (1), 40 (2), 45 (1), 41 (1) Mode = 38 and 40 (bimodal).
Fast Food 2: Delivery times: 40 (5), 37 (1), 41 (2), 38 (1), 46 (1) Mode = 40 (unimodal).

Thus Fast Food 1 does not have exactly one mode as stated (it's bimodal), so the fourth statement is false.

Conclusion

The false statement is: "Both fast food restaurants have the same mean delivery time of 40 minutes."