Question

It is believed that 43% of the US population can play the piano, 28% can play the guitar, 15% can play the harmonica, 12% can play the drums, and 2% can play other instruments. You want to take a simple random sample of individuals to test this claim. What is the smallest number of people required for the sample to meet the conditions for performing inference

Answer 1

Answer:

The smallest sample size to satisfy the conditions is n=500.

Step-by-step explanation:

The condition for performing the inference related to the sample size is that, for all the categories, the expected success and failures in the sample are at least 10:

$np\geq10\\\\n(1-p)\geq10$

The largest sample size required will be for the minimum p or (1-p).

This happens to be the proportion that can play other instruments: 2%.

Then, we can calculate the minimum sample size as:

$np\geq10\\\\n(0.02)\geq10\\\\n\geq(10/0.02)\\\\n\geq500$