Question

In a previous​ year, 61​% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 750 females aged 15 and older and finds that 456 are living alone. Is there sufficient evidence at the alphaequals0.01 level of significance to conclude the proportion has​ changed? Determine the​ P-value for this hypothesis test.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.61

H_a : p 0.61

= x / n = 456/750 = 0.608

P₀ = 0.61

1 - P₀ = 1- 0.61 = 0.39

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

=0.608-0.61 / [0.61*(0.39) /750 ]

= -0.112

P(z <-0.112 ) = 0.9106

P-value = 0.9106

= 0.01   

p=0.9106 ≥ 0.01

Reject the null hypothesis .

There is not enough evidence to claim that the population proportion p is different than p₀, at the α=0.01 significance level