Question

2. In a random sample of 1,971 homeowners, 414 had purchased their home within the past year. Five years ago, 10% of homeowners had purchased their home within the past year. Using ? = .01, find the population mean of homeowners who had purchased their home within the past year.

A. 16.96B. 16.27C. 15.96D. 16.48

Find the p-value of the test
H0 : ? = 100 when H? : ? > 100 and z = 2.17

A. .0199B. .0150C. .0193D. .0251

Answer 1

Solution :

Given that,

n =1971

x = 414

$\hat p$ = x / n = 414 / 1971 = 0.210

P₀ = 0.10

1 - P₀ = 1 - 0.10 = 0.90

$\alpha$ = 0.01

nP₀ (1 - P₀) = 0.10 * 0.90 = 0.900  

z = $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.210 - 0.10 / [$\sqrt$(0.10 * 0.90) / 1971

= 16.27

Option B. is correct.

This is the right tailed test .

P(z > 2.17) = 1 - P(z < 2.17) = 1 - 0.9850 = 0.0150

Pvalue = 0.0150

Option B. is correct.