Question

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

For example, you may like to estimate the population proportion of adults in the US who own SUVs. The data could be that you researched online by looking at a local dealership to find that 142 of the 432 vehicles sold are SUVs. You want to calculate a 90% (or another level) confidence interval for the population proportion. Assume a random sample.

For your response to a classmate (two responses are required, one in each option), solve a classmate’s confidence interval problem using a confidence level not previously used for that specific classmate’s problem. Make sure that you use appropriate terminology to state the problem and explain your solution.

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).