Question

Think about a population proportion that you may be interested in and propose a confidence interval problem for this parameter.

Answer 1

Answer: The confidence interval would be (0.2928,0.3672).

Step-by-step explanation:

Since we have given that

Total number of vehicles = 432

Number of SUVs sold = 142

So, it becomes,

$\hat{p}=\dfrac{x}{n}=\dfrac{142}{432}=0.33$

At 90% confidence interval,

z = 1.645

So, the confidence interval would be

$\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.33\pm 1.645\sqrt{\dfrac{0.33\times 0.67}{432}}\\\\=0.33\pm 0.0372\\\\=(0.33-0.0372,0.33+0.0372)\\\\=(0.2928,0.3672)$

Hence, the confidence interval would be (0.2928,0.3672).