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
