Question

In a previous​ year, 52​% of females aged 15 years of age and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 600 females aged 15 years of age and older and finds that 324 are living alone. Is there sufficient evidence at the alphaequals 0.1 level of significance to conclude the proportion has​ changed?

Answer 1

Answer)

Null hypothesis Ho : P = 0.52 (52%)

Alternate hypothesis Ha : P not equal to 0.52

N = 600

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 312

N*(1-p) = 288

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 324/600

Claimed P = 0.52

N = 600

After substitution

Test statistics z = 0.98

From z table, P(z>0.98) = 0.1635

But our test is two tailed

So, P-Value is = 2*0.1635 = 0.327

As the obtained Pvalue is greater than 0.1 (given significance level)

We fail to reject the Ho

So we do not have enough evidence to conclude that this percentage is different today