Question

An iPhone worth $3000 depreciates at ______ per year.

A) 5%
B) 10%
C) 15%
D) 20%

Answer 1

To calculate the 97 percent confidence interval for the percentage of students who own both an iPod and a smartphone, we use the sample proportion of 68 percent from 300 students and apply the confidence interval formula, incorporating the z-score for a 97% confidence level, which approximately equals 2.17.

Step-by-step explanation:

The question provided by the student requires us to calculate a confidence interval for the true percentage of students who own both an iPod and a smartphone. To solve this, we use the formula for a confidence interval which is p ± z*sqrt(p(1-p)/n), where p is the sample proportion, z is the z-score corresponding to the desired confidence level, and n is the sample size. We are given that 68% of the 300 students surveyed said they own both devices. Thus, our sample proportion (p) is 0.68 and our sample size (n) is 300.

To find the z-score for a 97% confidence level, we would typically use a z-score table or calculator, but for this example, we will assume that the z-score is approximately 2.17 (since this is a standard value that corresponds to a 97% confidence level).

The calculation steps are as follows:

1. Calculate the standard error: SE = sqrt(p(1-p)/n) = sqrt(0.68(1-0.68)/300)
2. Find the margin of error: ME = z*SE = 2.17 * sqrt(0.68(1-0.68)/300)
3. Compute the confidence interval: CI = p ± ME = 0.68 ± (2.17 * sqrt(0.68(1-0.68)/300))

After these calculations, the confidence interval provides an estimate for the true percentage of all students who own an iPod and a smartphone with 97% confidence.