A recent study of 750 Internet userd in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet?
A)0.321<p<0.379
B)0.316<p<0.384
C)0.309<p<0.391
D)0.305<p<0.395
To calculate the 95% confidence interval for the true proportion of women in Europe who use the Internet, we can use the formula:
Confidence interval = sample proportion ± (critical value) * (standard error)
First, let's calculate the sample proportion:
Sample proportion = 35% = 0.35
Next, we need to calculate the critical value. The critical value corresponds to the desired level of confidence, which in this case is 95%. For a 95% confidence level, the critical value is approximately 1.96.
Now, we need to calculate the standard error. The formula for the standard error of a proportion is:
Standard error = √[(sample proportion * (1 - sample proportion)) / sample size]
Sample size = 750
Using the formula, we get:
Standard error = √[(0.35 * (1 - 0.35)) / 750]
Calculating this, we find:
Standard error ≈ 0.016
Now, we can substitute the values into the confidence interval formula:
Confidence interval = 0.35 ± (1.96 * 0.016)
Calculating the confidence interval, we get:
Confidence interval ≈ 0.35 ± 0.031
So, the 95% confidence interval for the true proportion of women in Europe who use the Internet is approximately 0.319 to 0.381.
Comparing this to the given options, the correct answer is:
A) 0.321 < p < 0.379