Question

A random sample of 829 births included 431 boys. Use a 0.05 significance level to test the claim that 50.6 % of newborn babies are boys. Do the results support the belief that 50.6 % of newborn babies are boys? Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0 : pequals0.506 Upper H 1 : pgreater than0.506 B. Upper H 0 : pequals0.506 Upper H 1 : pnot equals0.506 Your answer is correct.C. Upper H 0 : pequals0.506 Upper H 1 : pless than0.506 D. Upper H 0 : pnot equals0.506 Upper H 1 : pequals0.506

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is nothing. (Round to two decimal places as needed.)

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.506

H_a : p 0.506

n = 829

x = 431

= x / n = 431 / 829 = 0.5199

P₀ = 0.506

1 - P₀ = 1 - 0.506 = 0.494

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.5199 - 0.506 / [(0.506 * 0.494) / 829]

= 0.80

Test statistic = 0.80