\# Previous Answer (0.785,0897) A town baseball organization is trying to figure out how many gloves to purchase for its lefthanded players. To help determine the oroportion of lefthanded kids in town, they conduct a random same of 92 kids. Il are efthanded. Construct a \( 98 \% \) confidence nterval for the proportion of kids who are efthanded.

To construct a \( 98\% \) confidence interval for the proportion of left-handed kids, you can use the formula: \[ \hat{p} \pm z \times \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \] Where \( \hat{p} = \frac{x}{n} \) (sample proportion), \( x \) is the number of left-handed kids, \( n \) is the total sample size, and \( z \) is the z-value corresponding to the confidence level. For \( 98\% \), the z-value is approximately \( 2.33 \). With \( x = 15 \) and \( n = 92 \): 1. Calculate \( \hat{p} = \frac{15}{92} ≈ 0.163 \). 2. Calculate the standard error: \[ SE = \sqrt{\frac{0.163(1 - 0.163)}{92}} ≈ 0.049 \] 3. Construct the interval: \[ 0.163 \pm 2.33 \times 0.049 \] This results in a confidence interval of approximately \( (0.066, 0.260) \). Now, how about some fun insights? Did you know that historically, left-handedness was often viewed with suspicion? In many cultures, left-handed individuals were thought to possess magical or even sinister traits, leading to a variety of stigmas and superstitions surrounding them! Fortunately, in modern times, left-handedness is celebrated, with entire products—like left-handed baseball gloves—designed just for those special southpaws! Investing in left-handed gloves is not just a smart move for a baseball organization; it's crucial in promoting inclusivity in sports. Having the right gear can influence a child's willingness to participate, boosting their confidence and enjoyment! Encouraging not just their skills but their love for the game fosters a sense of community and support among all young athletes. Plus, who doesn't love a little friendly competition? ⚾