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Use the table to answer the question.

Comparison of Shopping Time Between Group A and Group B
Group A 18 20 46 34 58 31 41
Group B 15 21 32 42 29 57 39
The table shows the times, in minutes, spent shopping by two different groups. First find the mean times each group spent shopping. Then determine the difference in the mean times. Round your answers to one decimal place.(2 points)
The mean time Group A spent shopping is ___ minutes.
The mean time Group B spent shopping is ___ minutes.
The mean times Group A and Group B spent shopping differ by _____ minutes.

1 answer

To find the mean times for Group A and Group B, we begin by calculating the mean for each group.

Group A: Times spent shopping: 18, 20, 46, 34, 58, 31, 41

  1. Calculate the sum: \( 18 + 20 + 46 + 34 + 58 + 31 + 41 = 248 \)

  2. Count the number of observations: There are 7 observations.

  3. Calculate the mean: \[ \text{Mean for Group A} = \frac{248}{7} \approx 35.4 \text{ minutes} \]

Group B: Times spent shopping: 15, 21, 32, 42, 29, 57, 39

  1. Calculate the sum: \( 15 + 21 + 32 + 42 + 29 + 57 + 39 = 235 \)

  2. Count the number of observations: There are 7 observations.

  3. Calculate the mean: \[ \text{Mean for Group B} = \frac{235}{7} \approx 33.6 \text{ minutes} \]

Difference in Mean Times: To find the difference in means: \[ \text{Difference} = \text{Mean for Group A} - \text{Mean for Group B} \] \[ \text{Difference} = 35.4 - 33.6 \approx 1.8 \text{ minutes} \]

Final Answers:

  • 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.