Question

Alcohol Consumption In a Gallup poll, 1011 adults were asked if they consume alcoholic beverages, and 64% of them said that they did. Construct a 90% confidence interval estimate of the proportion of all adults who consume alcoholic beverages. Can we safely conclude that the majority of adults consume alcoholic beverages?

Answer 1

To construct the 90% confidence interval for the proportion of all adults who consume alcohol, calculate the sample proportion (0.64), standard error, the critical value for 90% confidence, and the margin of error. The confidence interval is the point estimate plus or minus the margin of error. Based on the confidence interval and sample proportion, we can safely conclude that the majority of adults consume alcoholic beverages.

Step-by-step explanation:

Confidence Interval Estimate Calculation

To construct a 90% confidence interval estimate for the proportion of all adults who consume alcoholic beverages from the given Gallup poll where 64% of 1011 adults said they consume alcohol, we follow these steps:

1. Calculate the point estimate, p, which is the sample proportion (0.64).
2. Find the standard error (SE) of the proportion using the formula SE = √p(1 - p)/n, where n is the sample size.
3. Determine the critical value (z*) for a 90% confidence level.
4. Calculate the margin of error (ME) using the formula ME = z* × SE.
5. The confidence interval (CI) is then p ± ME.

Following these steps and noting that the proportion of adults that consume alcohol is above 50%, we can safely conclude that the majority of adults consume alcoholic beverages.