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)

3.Now press Enter in calculator to view answer

invNorm(0.01) = - 2.575

|Z | score for 98 % confidence interval 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 n Substituting , E, p and q in .

So the sample size n is 663.

Here we are planning a study to generate a 95% confidence interval for the unknown population proportion, p. The equation to determine the sample size for determining p seems to require knowledge of p, but this is obviously this is a circular argument, because if we knew the proportion of successes in the population, then a study would not be necessary! What we really need is an approximate value of p or an anticipated value. The range of p is 0 to 1, and therefore the range of p(1-p) is 0 to 1. The value of p that maximizes p(1-p) is p=0.5. Consequently, if there is no information available to approximate p, then p=0.5 can be used to generate the most conservative, or largest, sample size.