Question

Canadians Stream Music In a random sample of 3500 Canadian consumers, about \(71 \%\) report that they regularly stream music. \(^{25}\) (a) Is the sample likely to be representative of all Canadian consumers? Why or why not? (b) Is it reasonable to generalize this result and estimate that about \(71 \%\) of all Canadian consumers regularly stream music?

Short answer

Without detailed information, it's hard to definitively state if the sample is perfectly representative of all Canadian consumers. But considering it's a random, large sample, it's reasonable to assume a certain level of representativeness. Based on this sample, it's reasonable to estimate that about 71% of all Canadian consumers regularly stream music, but always with an understanding of a possible margin of error.

Step-by-step solution

Evaluation of Sample Representativeness

The representativeness of the sample depends on how it has been collected. If it's a random sample, it reduces the bias and hence, increases representativeness. The question does mention that it is a random sample, but it doesn't provide information about how the sample was selected, such as the age, location, or preferences of the music listeners, among other factors, which might influence music streaming behaviours.

Consideration of Sample Size

The sample size also affects the representativeness. The larger the sample, the more likely it is to be representative of the entire population. In this case, the sample size is 3500 which is a fairly large size and should be relatively representative of the general population if sampled correctly.

Considering generalizability of the result

With any statistic based on a sample, there is some risk when generalizing to the entire population. 71% of the sample size of 3500 suggests about 2485 people regular stream music. Based on these data, it's an informed assumption, though it's important to note that with any estimate, there is always a margin of error. Without knowing the margin of error, it's hard to say exactly how many Canadian consumers stream music, but 71% is our best estimate at this time.