Question

In a survey of 1,000 randomly selected adults in the United States, participants were asked what their most favorite and least favorite subjects were when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often than any other subject in both categories. Math was chosen by 230 of the 1,000 as their most favorite subject and chosen by 370 of the 1,000 as their least favorite subject.

a. Construct and interpret a 95% confidence interval for the proportion of U.S. adults for whom math was their most favorite subject.

b. Construct and interpret a 95% confidence interval for the proportion of U.S. adults for whom math was their least favorite subject.

Answer 1

To construct a confidence interval for the proportion of U.S. adults who chose math as their most or least favorite subject, calculate the sample proportion, standard error, and use the Z-score table for the critical value. Plug in the values to calculate the lower and upper bounds of the confidence interval.

Step-by-step explanation:

To construct a confidence interval for the proportion of U.S. adults for whom math was their most favorite subject, we can use the sample proportion and standard error formula. The sample proportion is calculated by dividing the number of adults who chose math as their most favorite subject (230) by the total number of adults surveyed (1,000). The standard error can be calculated using the formula: sqrt((p*(1-p))/n), where p is the sample proportion and n is the sample size. With a 95% confidence level, we can use the Z-score table to find the critical value. The formula for the confidence interval is: p +/- Z*(sqrt((p*(1-p))/n)). By plugging in the values, we can calculate the lower and upper bounds of the confidence interval.

For the proportion of adults who chose math as their least favorite subject, the process is the same. We calculate the sample proportion by dividing the number of adults who chose math as their least favorite subject (370) by the total number of adults surveyed (1,000). We can then calculate the standard error using the same formula as before. By finding the critical value from the Z-score table and using the formula for the confidence interval, we can calculate the lower and upper bounds of the confidence interval.