Final answer:
The question deals with confidence intervals and sampling error in estimating population proportion. No specific calculations are given, but the approach involves using a sample to estimate the true proportion with a certain degree of confidence. Ways to alter precision, such as adjusting the sample size or the confidence level, are also discussed.
Step-by-step explanation:
The subject of the question pertains to the statistical concept of confidence intervals and sampling error in proportion estimation.
The sampling error of p is the difference between the sample proportion and the true population proportion. In this instance, the student believes the true proportion (p) of first-time customers is 0.36.
The sampling error cannot be precisely calculated without additional information, such as the sample proportion; however, the standard deviation of the sampling distribution can be calculated assuming the president's belief is correct.
The margin of error refers to the level of precision desired for the estimate of the sample proportion, and it is influenced by the confidence level selected and the calculated standard deviation.
A common confidence level used is 95 percent, but other levels like 90 percent or 99 percent can also be applied depending on the required certainty.
Reducing the sampling error could be achieved by increasing the sample size.
The larger the sample, the closer the sample proportion is likely to be to the actual population proportion.
A reported sampling error of ±3 percent indicates that there is a 95 percent chance that the true population proportion falls within 3 percentage points of the sample proportion stated.