To calculate the mean shopping time for each group, we will first sum the times and then divide by the number of values in each group.
Group A: Times: 18, 20, 46, 34, 58, 31, 41
Sum of Group A: \[ 18 + 20 + 46 + 34 + 58 + 31 + 41 = 248 \]
Number of values in Group A: 7
Mean time for Group A: \[ \text{Mean} = \frac{248}{7} \approx 35.4 \text{ minutes} \]
Group B: Times: 15, 21, 32, 42, 29, 57, 39
Sum of Group B: \[ 15 + 21 + 32 + 42 + 29 + 57 + 39 = 235 \]
Number of values in Group B: 7
Mean time for Group B: \[ \text{Mean} = \frac{235}{7} \approx 33.6 \text{ minutes} \]
Now, we will determine the difference in the mean times:
Difference: \[ 35.4 - 33.6 = 1.8 \text{ minutes} \]
In conclusion:
- The mean time Group A spent shopping is 35.4 minutes.
- The mean time Group B spent shopping is 33.6 minutes.
- The mean times Group A and Group B spent shopping differ by 1.8 minutes.