Question

According to a Mobile Marketing Company random survey of 2,000 respondents, 55% of the respondents stated they text while driving. Using this information, the 95% confidence interval for the population proportion, p, of mobile phone users that text while driving is:

Answer 1

To find the 95% confidence interval for the population proportion, we can use the formula:

CI = p ± z*(sqrt(p*(1-p)/n))

where CI is the confidence interval, p is the sample proportion, z is the z-score for the level of confidence (which is 1.96 for 95% confidence interval), and n is the sample size.

Given that the sample proportion (p) is 0.55 (55%), the sample size (n) is 2,000, and the z-score for 95% confidence interval is 1.96, we can plug in these values into the formula and get:

CI = 0.55 ± 1.96*(sqrt(0.55*(1-0.55)/2000))

Simplifying the expression inside the square root, we get:

CI = 0.55 ± 0.032

So the 95% confidence interval for the proportion of mobile phone users that text while driving is:

CI = [0.518, 0.582]

Therefore, we can say with 95% confidence that the true proportion of mobile phone users who text while driving falls somewhere between 51.8% and 58.2%.

Explanation: