Question

ali and diane want to find the mean number of movies students in their class saw last year. so they each randomly select students in their class and ask for the numbers.
the results are shown below. use the data to answer the questions.
alis sample:
9, 12, 13, 14, 15
dianes sample:
13, 6, 7, 5, 8, 14
(a) what is the sample size for alis sample?
(b) what is the sample size for dianes 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?
alis sample dianes sample
why?
it has the smaller sample size.
it has the larger sample size.
it has the smaller mean.
it has the larger mean.

Explanation:

Step1: Count the number of data points in Ali's sample

Ali's sample: \(9, 12, 13, 14, 15\). The number of data points is \(n = 5\).

Step2: Count the number of data points in Diane's sample

Diane's sample: \(13, 6, 7, 5, 8, 14\). The number of data points is \(n = 6\).

Step3: Analyze the sample - size and its relation to estimating the mean

In general, a larger sample size (assuming random sampling) is more likely to give a good estimate of the population mean. Since \(5<6\) (Ali's sample size \(n = 5\) and Diane's sample size \(n = 6\)), Diane's sample has a larger sample size.

Answer:

(a) \(5\)
(b) \(6\)
(c) Diane's sample; It has the larger sample size.