Question

You take a random sample of 419 Galaxy phones off an assembly line and find 0.12 proportion to be defective. What is a lower bound for a 90% confidence interval for the proportion of defective Galaxy phones from this assembly line

Answer 1

Answer:

The lower bound for a 90% confidence interval for the proportion of defective Galaxy phones from this assembly line is 0.0939.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$, and a confidence level of $1-\alpha$, we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$.

For this problem, we have that:

$n = 419, p = 0.12$

95% confidence level

So $\alpha = 0.1$, z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$, so $Z = 1.645$.

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 - 1.645\sqrt{\frac{0.12*0.88}{419}} = 0.0939$

The lower bound for a 90% confidence interval for the proportion of defective Galaxy phones from this assembly line is 0.0939.