Final answer:
A 99% confidence interval for the mean number of soft drinks consumed by teenagers can be calculated using statistical methods, with considerations for sampling size and accuracy. Telephone and mailed surveys may present challenges like low response rates and bias, but can be mitigated with thoughtful survey design and follow-up strategies.
Step-by-step explanation:
To construct a 99% confidence interval for the mean number of soft drinks consumed by teenagers each week, statistical methods will be employed. The confidence interval can be calculated using the sample mean, standard deviation, and the Z-value corresponding to the 99% confidence level from the standard normal distribution. For a precise confidence interval, it's crucial to have a representative sample and accurate data.
If we are using the provided information about the amount of sugar in cans of soda with a known mean and standard deviation, we would first verify if the sample size is large enough for a normal distribution approximation. Since a sample size of 100 is generally considered sufficient for the Central Limit Theorem to apply, we could proceed with the confidence interval calculation, adjusting for the fact that we are seeking information about the number of soft drinks consumed, not sugar content.
Difficulties in collecting accurate data from telephone or mailed surveys can include low response rates, sampling bias, and inaccurate responses. To overcome these problems, researchers might use strategies such as reminder calls or emails, offering incentives for participation, and designing questions to be as clear and unbiased as possible.