Of 290 employees selected randomly from one company,12.41% of them commute by carpooling.Construct a 90% confidence interval for the percentage of all employees of the company who carpool.

A) (7.90%,16.9%)
B) (8.61%,16.2%)
C) (9.22%,15.6%)
D) (7.90%,17.4%)
E) (7.41%,17.4%)

Question

Stephano Sphanzzz · Accepted Answer

Final Answer : C, Explanation :  To construct a 90% confidence interval for the percentage of all employees who carpool, we can use the formula:point estimate +/- z* (standard error)where the point estimate is the observed percentage of employees who carpool (12.41% or 0.1241), z* is the z-score corresponding to a 90% confidence level (which we can find using a z-table or calculator, and is approximately 1.645), and the standard error is calculated as:sqrt[(point estimate * (1 - point estimate)) / n]where n is the sample size (290). Substituting these values, we get:0.1241 +/- 1.645 * sqrt[(0.1241 * (1 - 0.1241)) / 290]Simplifying, we get:0.1241 +/- 0.029So the 90% confidence interval is (0.1241 - 0.029) to (0.1241 + 0.029), or 0.0951 to 0.1531. Converting to percentages, we get (9.51% to 15.31%) or (9.22% to 15.6%) rounded to two decimal places. The closest answer choice is C: (9.22%, 15.6%).

Of 290 employees selected randomly from one company,12.41% of them commute by carpooling.Construct a 90% confidence interval for the percentage of all employees of the company who carpool.

A) (7.90%,16.9%)
B) (8.61%,16.2%)
C) (9.22%,15.6%)
D) (7.90%,17.4%)
E) (7.41%,17.4%)

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Of 290 employees selected randomly from one company,12.41% of them commute by carpooling.Construct a 90% confidence interval for the percentage of all employees of the company who carpool.A) (7.90%,16.9%) B) (8.61%,16.2%) C) (9.22%,15.6%) D) (7.90%,17.4%) E) (7.41%,17.4%)

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Related questions

Of 290 employees selected randomly from one company,12.41% of them commute by carpooling.Construct a 90% confidence interval for the percentage of all employees of the company who carpool.

A) (7.90%,16.9%)
B) (8.61%,16.2%)
C) (9.22%,15.6%)
D) (7.90%,17.4%)
E) (7.41%,17.4%)