Question

(a) Write the claim mathematically and identify Ho and Ha.

(b) Find the critical value(s) and identify the rejection region(s).

(c) Find the standardized test statistic.

(d) Decide whether to reject or fail to reject the null hypothesis.

In a sample of 1000 home buyers, you find that 413 home buyers found their real estate agent through a friend. At alphaαequals=.06 can you reject the claim that 46% of home buyers find their real estate agent through a friend?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.46

H_a : p 0.46

n = 1000

x = 413

= x / n = 413 / 1000 = 0.413

P₀ = 0.46

1 - P₀ = 1 - 0.46 = 0.54

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.413 - 0.46 / [(0.46 * 0.54) / 1000]

= -2.98

Test statistic = -2.98

Z_.03 = 1.88

Critical values : +/-1.88

Test statistic > critical value

Reject the null hypothesis .