Respuesta :
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:
[tex]np\geq10\\\\n(1-p)\geq10[/tex]
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:
[tex]np\geq10\\\\n(0.02)\geq10\\\\n\geq(10/0.02)\\\\n\geq500[/tex]
Answer:
250
Step-by-step explanation:
Remember there are 2 conditions to perform a goodness of fit chi-test:
Simple random sample: The data must come from a random sample or a randomized experiment.
Expected counts: All expected counts are at least five. You must state the expected counts.
To explain expected counts a bit better, imagine I surveyed 100 people about their ice cream preferences. Before beginning it is believed that 50% like chocolate, 47% like vanilla, and 3% like strawberry.
That means our expected counts are:
100(.50) = 50
100(.47) = 47
100(.03) = 3
This is a problem, because 3 < 5 and so we can not perform a goodness of fit chi-test.
So how do you find the minimum sample size? Use this formula:
sample size (n) * smallest proportion (p) = 5
In the context of ice cream:
n*.03 = 5
n = 5 / .03
n = 167 (because you can't interview 2/3s of a person)
In the context of the problem:
n* .02 = 5
n = 5 / 0.02
n = 250
This means we need to sample at least 250 people to meet our expected count condition.
