As manager for an advertising company, you must plan a...

As manager for an advertising company, you must plan a campaign designed to increase Twitter usage. You want to first determine the percentage of adults who know what Twitter is. How many adults must you survey in order to be 90% confident that your estimate is within five percentage points of the true population percentage? a. Assume that nothing is known about the percentage of adults who know what Twitter is. b. Assume that a recent survey suggests that about 85% of adults know what Twitter is (based on a Pew Research Center survey). c. Given that the required sample size is relatively small, could you simply survey the adults at the nearest college?

As manager for an advertising company, you must plan a campaign designed to increase Twitter usage. You want to first determine the percentage of adults who know what Twitter is. How many adults must you survey in order to be 90% confident that your estimate is within five percentage points of the true population percentage?
a. Assume that nothing is known about the percentage of adults who know what Twitter is.
b. Assume that a recent survey suggests that about 85% of adults know what Twitter is (based on a Pew Research Center survey).
c. Given that the required sample size is relatively small, could you simply survey the adults at the nearest college?

Key Concepts

Confidence Level

The confidence level indicates the degree of certainty that the true population parameter lies within the calculated confidence interval. In the context of estimating a proportion, a 90% confidence level means that if we repeated the survey many times, we would expect about 90% of the calculated intervals to contain the actual proportion.

Margin of Error

The margin of error is the maximum expected difference between the true population proportion and the sample estimate. It quantifies the level of precision of the estimate; a five percentage point margin of error implies that the survey results will be within plus or minus 5% of the true proportion, with the designated level of confidence.

Sample Size Calculation for Proportions

Determining the required sample size for estimating a population proportion involves using a formula that incorporates the desired confidence level, the margin of error, and an estimate of the population proportion. In the absence of prior knowledge, a conservative estimate (50%) is typically used to maximize the estimated variance, ensuring that the sample size is appropriately large.

Conservative Estimation

Conservative estimation is a strategy used in sample size calculations when there is uncertainty about the true population proportion. By assuming a proportion of 50%, which yields the maximum variance, the resulting sample size ensures that the estimate will be sufficiently precise regardless of the actual proportion.

Representativeness and Convenience Sampling

Ensuring a representative sample is crucial for generalizing survey results to the overall population. Convenience sampling, such as surveying adults at a nearby college, may introduce bias since the sample may not accurately reflect the diverse characteristics of the broader adult population. Proper random sampling techniques are typically preferred to achieve a more accurate estimate.

Transcript

Please give Ace some feedback