The federal government would like to estimate the proportion of households in the U. S. population that own their own homes. A pilot sample of 40 households found that 24 of them owned their homes. Determine the number of households that need to be sampled to construct a 99% interval with a margin of error equal to 3% to estimate the proportion.

1770

Step-by-step explanation:

We need to estimate number of households to be sampled to construct a 99% confidence interval.

Number of households to be sampled=n=?

The proportion can be estimated as

p=x/n.

We know that 24 out of 40 households owns their home.

so, x=24 and n=40.

p=24/40

p=0.6

q=1-p=1-0.6=0.4

pq=0.6*0.4=0.24

E=0.03

n=1769.56.

n=1770.

Thus, the number of households that need to be sampled are 1770.

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step-by-step explanation: