Question

Two​ researchers, Jaime and​ Mariya, are each constructing confidence intervals for the proportion of a population who is​ left-handed. They find the point estimate is . Each independently constructed a confidence interval based on the point​ estimate, but​ Jaime's interval has a lower bound of and an upper bound of ​, while​ Mariya's interval has a lower bound of and an upper bound of . Which interval is​ wrong? Why? Choose the correct answer below.

Answer 1

Complete question :

Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is 0.13. Each independently constructed a confidence interval based on the point estimate, but Jaime’s interval has a lower bound of 0.097 and an upper bound of 0.163, while Mariya’s interval has a lower bound of 0.117 and an upper bound of 0.173. Which interval is wrong? Why?

Answer:

Mariya's interval

Step-by-step explanation:

Point estimate = 0.13

Mariya's confidence interval :

Lower boundary = 0.117

Upper boundary = 0.173

Jamie's confidence interval :

Lower boundary = 0.097

Upper boundary = 0.163

The correct confidence interval should have an average value equal to the value of the point estimate ;

Jamie's confidence interval average :

(0.097 + 0.163) / 2 = 0.26 / 2 = 0.13

Mariya's confidence interval average :

(0.117 + 0.173) / 2 = 0.29 / 2 = 0.145

Based on the confidence interval average obtained we can conclude that Mariya's interval is wrong as it the average obtained is greater than the point estimate.

0.145 > 0.13