Question

In a previous​ year, 58​% of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 650 females aged 15 and older and finds that 367 are living alone. Is there sufficient evidence at the alphaαequals=0.01 level of significance to conclude the proportion has​ changed?

Answer 1

H0: p = 0.58

Ha: p 0.58

Sample proprotion = 367 / 650 = 0.5646

Test statistics

z = ( - p) / sqrt [ p( 1 - p) / n ]

= ( 0.5646 - 0.58) / sqrt ( 0.58 * ( 1 - 0.58) / 650 )

= -0.80

Critical values at 0.01 significance level = -2.576 , 2.576

Since test statistics falls in non-rejection region, fail to reject H0.

We do not have sufficient evidence to support the claim that the proportion has​ changed.