Question

In a recent year, 125.8 million adults, or 58.6% of the adult American population, were married. In a New England town, a simple random sample of 1,445 adults includes 56.1% who are married. Test the claim that this sample comes from a population with a married percentage of less than 58.6%. Use a 0.05 significance level and conduct a full hypothesis test using the six-step process.

Answer 1

We have given :

n = sample size = 1445 random sample of adults

phat = sample proportion = 56.1 % = 0.561

p = population proportion = 58.6 % = 0.586

α = significance level =  0.05  

Claim :

Test the claim that this sample comes from a population with a married percentage of less than 58.6%.

Step 1  : To test :

Ho : p = 0.586  VS H1 : p <  0.586

## Step 2 :

Test Statistics :

z = ( phat - p ) / SQRT( p * (1-p) / n)

z = ( 0.561 - 0.586 ) / SQRT ( 0.586 * 0.414  / 1445 )

z = - 0.025 / 0.0129573

z = - 1.9294

## Step 3 :

## α = level of significance value = 0.05

## Step 4 : p value

p value = P [ z > 1.57 ]

= P [ z < -1. 9294  ]

( now use table )

= 0.0268

## Step 5 :  

Decision :

We reject Ho if p value is less than α value using p value approach
here p value is less than α value we reject Ho at given level of significance .

## Step 6 :

Conclusion :

There is sufficient evidence to conclude that this sample comes from a population with a married percentage of less than 58.6%.