According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing H0: p = 0.173 versus Ha: p < 0.173. The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth graders surveyed had used marijuana. Is the sample size condition for conducting a hypothesis test for a population proportion satisfied? No, because 80 students is not enough to be representative of the students in the school district. Yes, because (80)(.173) and (80)(1 ‑ 0.173) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions. 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. Yes, because the sample is random. It represents the 8th graders in the district.

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