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.

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.