Diane and Melissa want to find the mean amount of time it takes students in their class to travel to school. So they each randomly select students in their class and ask for the times.The results are shown below (in minutes). Use the data to answer the questions.Diane's sample:7, 5, 20, 12, 16, 6, 8Melissa's sample:13, 8, 12, 20, 7(a) What is the sample size for Diane's sample?(b) What is the sample size for Melissa's sample?(c) Suppose you had to choose one sample to estimate the mean.Which sample is more likely to give a good estimate of the mean?Diane's sampleMelissa's sampleWhy?It has the smaller mean.It has the larger mean.It has the smaller sample size.It has the larger sample size.
Question
Diane and Melissa want to find the mean amount of time it takes students in their class to travel to school. So they each randomly select students in their class and ask for the times.The results are shown below (in minutes). Use the data to answer the questions.Diane's sample:7, 5, 20, 12, 16, 6, 8Melissa's sample:13, 8, 12, 20, 7(a) What is the sample size for Diane's sample?(b) What is the sample size for Melissa's sample?(c) Suppose you had to choose one sample to estimate the mean.Which sample is more likely to give a good estimate of the mean?Diane's sampleMelissa's sampleWhy?It has the smaller mean.It has the larger mean.It has the smaller sample size.It has the larger sample size.
Solution
(a) The sample size for Diane's sample is 7. This is because there are 7 different times listed in her sample.
(b) The sample size for Melissa's sample is 5. This is because there are 5 different times listed in her sample.
(c) It's not about which sample has the smaller or larger mean, or the smaller or larger sample size. The sample that is more likely to give a good estimate of the mean is the one that is more representative of the population. In this case, without additional information about the population, it's impossible to definitively say which sample is more representative. However, generally, a larger sample size can lead to a more accurate estimate of the population mean, so Diane's sample might be a better choice.
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