SOLUTION: The Dean of a college wants to use the proportion of a population to determine the sample size needed to interview regarding their thoughts about the new school structures.She want

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Question 1174399: The Dean of a college wants to use the proportion of a population to determine the sample size needed to interview regarding their thoughts about the new school structures.She want to be able to assert with a probability 0.95 that her error will be at most 0.05. Similar pols in the past showed that 65% approved the new structure. How large a sample does the Dean need?

Answer by CPhill(2189) (Show Source):
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**1. Identify the Parameters:**
* Confidence Level: 95% (This gives us a z-score of 1.96)
* Margin of Error (E): 0.05
* Estimated Population Proportion (p̂): 0.65 (from past polls)
* Estimated Population Proportion who don't approve (q̂) = 1 - p̂ = 0.35
**2. Use the Sample Size Formula:**
The formula for calculating the sample size (n) for estimating a population proportion is:
n = (z^2 * p̂ * q̂) / E^2
**3. Plug in the Values:**
n = (1.96^2 * 0.65 * 0.35) / 0.05^2
**4. Calculate:**
n ≈ 350.28
**5. Round Up:**
Since we cannot have a fraction of a person, always round the sample size up to the nearest whole number.
n = 351
**Therefore, the Dean needs a sample size of 351 students to achieve the desired level of confidence and margin of error.**