Questions: 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 0.19 . Each independently constructed a confidence interval based on the point estimate, but Jaime's interval has a lower bound of 0.117 and an upper bound of 0.263 , while Mariya's interval has a lower bound of 0.095 and an upper bound of 0.255 . Which interval is wrong? Why? Choose the correct answer below. A. Mariya's interval is wrong because it is not centered on the point estimate. B. Mariya's interval is wrong because it is too wide. C. Jaime's interval is wrong because it is too narrow D. Jaime's interval is wrong because it does not include the point estimate.

Solution Steps

The point estimate for the proportion of the population who is left-handed is \( p = 0.19 \). Two researchers, Jaime and Mariya, constructed confidence intervals based on this point estimate.

• Jaime's interval:

  • Lower bound: \( 0.117 \)
  • Upper bound: \( 0.263 \)

• Mariya's interval:

  • Lower bound: \( 0.095 \)
  • Upper bound: \( 0.255 \)

To determine if the intervals are centered around the point estimate, we calculate the center of each interval.

• Jaime's interval center: \[ \text{Center}_{\text{Jaime}} = \frac{0.117 + 0.263}{2} = \frac{0.380}{2} = 0.19 \]

• Mariya's interval center: \[ \text{Center}_{\text{Mariya}} = \frac{0.095 + 0.255}{2} = \frac{0.350}{2} = 0.175 \]

Now we compare the centers of the intervals with the point estimate \( p = 0.19 \).

• Jaime's interval center: \( 0.19 \) (matches the point estimate)
• Mariya's interval center: \( 0.175 \) (does not match the point estimate)

Since Mariya's interval center \( 0.175 \) is not equal to the point estimate \( 0.19 \), her interval is incorrect because it is not centered on the point estimate.

Final Answer