Respuesta :
Answer:
No
Step-by-step explanation:
We have:
n = 80,
p = 0.1 (10%)
q = 1 - p = 1 - 0.1 = 0.9
Usually we use
np > 5, and nq > 5, but this question is using
np > 10, so we'll use that. It means that the proportion times the sample size must be greater than 10, we have
80(0.1) = 8 and
80(0.9) = 72,
since we got 8 as one answer, the situation doesn't hold up.
Since the sample requires at least 10 successes and 10 failures, we have that the correct option is:
No, because (80)(.10) is less than 10. Because of this the sample size is too small to use the normal distribution to model the distribution of sample proportions.
To test an hypothesis for a proportion p in a sample of size n, it is needed that:
- There are at least 10 successes, that is, [tex]np \geq 10[/tex].
- There are at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex].
In this problem, there is a sample of 80, thus [tex]n = 80[/tex], and a proportion of 10%, thus [tex]p = 0.1[/tex]. Then:
[tex]np = 80(0.1) = 8 < 10[/tex]
Thus, the correct option is:
No, because (80)(.10) is less than 10. Because of this the sample size is too small to use the normal distribution to model the distribution of sample proportions.
A similar problem is given at https://brainly.com/question/24261244