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Answer :
Final answer:
To estimate the true proportion of Americans accessing the internet on their cell phones, with a 3% margin of error and 90% confidence level, we need a sample size of at least 708 people. This calculation assumes the sample will accurately represent the larger population, therefore using a larger, more conservative sample size is generally good practice.
Explanation:
To estimate the true proportion of Americans who access the internet on their cell phones within 3% with 90% confidence, we would use the formula for sample size in a proportion confidence interval, that is n = (Z^2 * p * (1-p)) / E^2.
Where Z is the corresponding Z-score for the confidence level (90%), p is the estimated proportion of the population in the preliminary study (82%), and E is the desired margin of error (3%).
Using these values, we have Z = 1.645 for 90% confidence level, p = 0.82, and E = 0.03. Substituting these into the sample size formula, we get; n = (1.645^2 * 0.82 * (1-0.82)) / 0.03^2 = 707.4. Round the answer to the next higher value as you can't have a fractional participant in a survey, therefore, the minimum sample size should be 708.
It's important to note that this calculation is based on the assumption that the sample will be a good representative of the population. It's always a good practice to use a conservative sample size for a better estimation of such proportion.
Learn more about Sample Size Calculation here:
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