after a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. the…

after a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. the service department randomly selects 50 cars on the dealership lot, examines them, and determines that 18 have damage. assuming all conditions have been met, they construct a 99% confidence interval for the true proportion of cars with damage from the storm. what are the calculations for this interval?\n0.36±2.58√(0.36(1 - 0.36)/50)\n0.64±2.33√(0.64(1 - 0.64)/50)\n0.36±2.33√(0.36(1 - 0.36)/50)\n0.64±2.58√(0.64(1 - 0.64)/50)

after a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. the service department randomly selects 50 cars on the dealership lot, examines them, and determines that 18 have damage. assuming all conditions have been met, they construct a 99% confidence interval for the true proportion of cars with damage from the storm. what are the calculations for this interval?\n0.36±2.58√(0.36(1 - 0.36)/50)\n0.64±2.33√(0.64(1 - 0.64)/50)\n0.36±2.33√(0.36(1 - 0.36)/50)\n0.64±2.58√(0.64(1 - 0.64)/50)

Answer

Explanation:

Step1: Calculate sample proportion

The sample proportion $\hat{p}=\frac{x}{n}$, where $x = 18$ (number of cars with damage) and $n=50$ (sample size). So $\hat{p}=\frac{18}{50}=0.36$.

Step2: Determine z - value for 99% confidence interval

For a 99% confidence interval, the critical z - value $z_{\alpha/2}=2.58$.

Step3: Recall the formula for confidence interval of a proportion

The formula for the confidence interval of a proportion is $\hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$. Substituting $\hat{p}=0.36$, $z_{\alpha/2}=2.58$ and $n = 50$ into the formula, we get $0.36\pm2.58\sqrt{\frac{0.36(1 - 0.36)}{50}}$.

Answer:

$0.36\pm2.58\sqrt{\frac{0.36(1 - 0.36)}{50}}$