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Statistics / Fundamentals of Statistics 4 / Chapter 9.1 / Problem 32AYU

Fundamentals of Statistics | 4th Edition | ISBN: 9780321838704 | Authors: Michael Sullivan,III

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QUESTION:

Sullivan Statistics Survey: Language One question on the Sullivan Statistics Survey is “Is a language other than English the primary language spoken in your home?” Treat the survey respondents as a simple random sample of adult Americans. Construct and interpret a 95% confidence interval for the proportion of adult Americans who speak a language other than English at home.

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QUESTION:

Sullivan Statistics Survey: Language One question on the Sullivan Statistics Survey is “Is a language other than English the primary language spoken in your home?” Treat the survey respondents as a simple random sample of adult Americans. Construct and interpret a 95% confidence interval for the proportion of adult Americans who speak a language other than English at home.

ANSWER:

Step 1 of 2

From the given information we have $\overline{x}$ =1.23, $\sigma{}=$ 0.65 and n = 1120. We need to find the 95% confidence interval and it is calculated by using the formula $\overline{x}\pm{}{Z}^{*}\frac{\sigma{}}{\sqrt{n}}$ .

${Z}^{*}$ = 1.96(from standard normal table)

Confidence Level	z? Multiplier
.90 (90%)	1.645
.95 (95%)	1.96
.98 (98%)	2.326
.99 (99%)	2.578

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