# Solve this problem.

(Use a TI-84)

A newspaper article about the results of a poll states: "In theory, the results of a poll states: "In theory, the result of such a poll, in 99 cases out of 100 should differ by no more that 5 percentage points in either direction from what would have been obtained by interviewing all voters in the United States," Find the sample size suggested by this statement.
asked Apr 17, 2015

Step 1:

Marginal error is 5% .[ In either directions ]

Find the sample size.

Formula for sample size is .

where  is the value from the standard normal distribution reflecting the confidence level.

is the desired margin of error,

p is the proportion of successes in the population,

q is the proportion of failure in the population.

Step 2:

Now find score for 99 cases out of 100.

Follow these steps to evaluate z score for top 99 cases out of 100.

1.Select invNorm() in Ti -84 calculator.

[ 2nd --> VARS --> 3 ]

2.Enter area in decimals .

invNorm((1 - 0.99)/2)

invNorm(0.005)

invNorm(0.005) = - 2.575

|Z | score for 99 cases out of 100 is 2.575.

Step 3:

Let consider the value  p is 0.5.

So the value of q is .

Marginal error is E = 0.05.

Now find sample size substituting , E, p and q in .

So the sample size is 663.

Solution :

The sample size is 663.

answered Apr 18, 2015
edited Apr 18, 2015