In Exercise 5.21, we learned that a Rasmussen Reports survey of 1,000 USadults found that 42% believe raising the minimum wage will help the economy. Construct a 99% confidence interval for the true proportion of US adults who believe this.

Final answer:

The 99% confidence interval for the proportion of US adults believing that raising the minimum wage will help the economy, based on a survey, is approximately (0.386, 0.454).

Explanation:

To compute the 99% confidence interval for the parameter of interest - the true proportion of adults believing that raising the minimum wage will help the economy - we use the formula for the confidence interval for a proportion: p ± Z*(sqrt((p(1 - p))/n)). Here p is the sample proportion, n is the sample size and Z* is the Z score corresponding to the desired confidence level, in this case 99%.

The given sample proportion (p) is 0.42 and the sample size (n) is 1000. The Z score for a 99% confidence interval is approximately 2.58.

Substituting these values into the confidence interval formula yields: 0.42 ± 2.58 * sqrt((0.42(1 - 0.42))/1000). After computation, we obtain the 99% confidence interval as (0.386, 0.454).  

Learn more about confidence interval here:

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