15. Foreign Language According to a study done by Wakefield esearch, the proport

Question

15. Foreign Language According to a study done by Wakefield esearch, the proportion of Americans who can order a meal in a foreign language is 0.47. (a) Suppose a random sample of 200 Americans is asked to disclose whether they can order a meal in a foreign language. Is the response to this question qualitative or quantitative? Explain. (b) Explain why the sample proportion, p, is a random variable. What is the source of the aiation of p, the proportion (c) Describe the sampling distribution of p, the proportion of Americans who can order a meal in a foreign language. Be sure to verify the model requirements. (d) In the sample obtained in part (a), what is the probability the proportion of Americans who can order a meal in a foreign language is greater than 0.5? (e) Would it be unusual that, in a survey of 200 Americans, 80 or fewer Americans can order a meal in a foreign language? Why?

Explanation / Answer

a)
Response is quantitative.
Because the respose would be yes or no which results into the number of people says yes or no.

b)
pcap is random variable because the random sample is selected from the population.
Source of variability is the sample size.

c)
Sampling distribution of pcap is normal with
mu(pcap) = pcap
and sd(pcap) = sqrt(pcap * (1-pcap)/n)

d)
sd = sqrt(0.47*0.53/200) = 0.0353

P(pcap > 0.5)
= P(z > (0.5 - 0.47)/0.0353)
= P(z > 0.8499)
= 0.1977 .. using right tailed z table

e)
pcap = 80/200 = 0.4

P(pcap < 0.4)
= P(z < (0.4 - 0.47)/0.0353)
= P(z < -1.983)
= 0.0237 .. using left tailed z table

This is unusual because probability is significantly less

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