Final answer:
To verify Zane's claim that 85% of his contacts have a local area code, we need to compare the proportions from his random samples to his claim. A confidence interval can be used to assess if sample data supports his assertion, considering potential sources of bias that could affect the outcome.
Step-by-step explanation:
To determine if Zane's claim that 85% of his contacts have a local area code is supported by the data from his samples, we need to assess the proportion of contacts with a local area code in each of the 5 samples of 20 contacts he makes. If the proportion of contacts with a local area code in each sample is consistent with his claim, we could say the data supports his claim. This method is similar to the ones used in statistical analysis for polling or market research, such as estimating cell phone ownership or the popularity of a certain type of phone.
For example, if a market research firm uses a 95% confidence level to determine the proportion of adults with cell phones and finds an estimated range that includes the assumed population proportion, they could assert that their estimate supports the belief about the population's phone ownership. Similarly, if the proportion of contacts with a local area code in Zane's samples closely aligns with 85%, this would support his claim. However, without the actual data from Zane's samples, we cannot definitively determine whether his claim is supported or not.
A principle to consider is the confidence interval. If the sample proportions are within the confidence interval around 85%, Zane's claim is more likely to be supported. Furthermore, it is important to consider potential sources of bias such as selection bias or non-representative sampling methods which could affect the validity of the results.