SECTION 8.2 Distribution of the Sample Proportion 413 ding plying the Concepts t

Question

SECTION 8.2 Distribution of the Sample Proportion 413 ding plying the Concepts tion( al) Foreign Language According to a study done by Wakefield Research, 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 variability? (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 (e) Would it be unusual that, in a survey of 200 Americans, 80 or 1 the proportion of Americans who can order a meal in a foreign language is greater than 0.5? fewer Americans can order a meal in a foreign language? Why? . Are You Satisfied? According to a studv done by the Gallup

Explanation / Answer

a)

Qualitative data is information about qualities; information that can't be measured.

While Quantitative is information that can be measured, written down with numbers.

Hence, the response variable in this case is Quantitative ie no of people who say yes can be counted as well no of people who no.

b)

Sample proportion is a random variable as the 200 People chosen for the study are chosen at random.

c)

The sample proportion of Americans who can order a meal in a foreign language is 0.47 ie if there were 100 people in America, then according to this study, 47 will be able to order food in a foreign language.

d)

p0 = 0.47

p = 0.5

z = (p-p0)/( p0*(1- p0)/n)1/2 = 0.85

P(X>p0) = P(z> 0.85) = 1-P(z<0.85) = 1-.8023 = 0.1977

e)

p = 80/200 = .4

z = (p-p0)/( p0*(1- p0)/n)1/2 = -1.98

P(x<.4) = P(z<-1.98) = 0.0239 or 2.39%

Since, this probability is very less, it is unusual.

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