Question

A researcher wishes to estimate, with 99% confidence, the
population proportion of adults who think the president of their
country can control the price of gasoline. Her estimate must be
accurate within 2% of the true proportion.

a) No preliminary estimate is available. Find the minimum
sample size needed.

b) Find the minimum sample size needed, using a prior study
that found that 32% of the respondents said they think their
president can control the price of gasoline.

c) Compare the results from parts (a) and (b).

Answer #1

**ANSWER::**

**a)**

When proportion is not specified, p = 0.50

Sample size n = Z^{2} P ( 1 - P) / E^{2}

Where E is error = 0.02

n = 2.5758^{2} * 0.5 * 0.5 / 0.02^{2}

= 4146.72

**Minimum sample size = 4147**

**b)**

**Samp**le size n = Z^{2} P ( 1 - P) /
E^{2}

n = 2.5758^{2} * 0.32 * 0.68 / 0.02^{2}

= 3609.28

**Minimum sample size = 3609**

**c)**

Sample size required is lower when proportion is given rather than proportion is unknown.

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