in order to estimate the mean amount of time computer users spend on the internet ea mn, how many people do i interview to have 90% confident sample mean within 11 min of the pop mean? Assum sd= 203 min
To estimate the mean amount of time computer users spend on the internet, you can use a confidence interval. The formula for the confidence interval is:
CI = X̄ ± Z * (σ/√n)
Where:
CI = Confidence Interval
X̄ = Sample Mean
Z = Z-Score (corresponding to the desired confidence level)
σ = Population Standard Deviation
n = Sample Size
In this case, you want a 90% confidence level and a margin of error of 11 minutes. The Z-Score corresponding to a 90% confidence level is 1.645 (you can look up this value in a standard normal distribution table or use a statistical software). The population standard deviation is given as 203 minutes.
11 = 1.645 * (203 / √n)
Now, let's solve the equation for the sample size (n):
√n = 1.645 * (203 / 11)
√n ≈ 30.35
n ≈ (30.35)^2
n ≈ 922.3225
Based on this calculation, you would need to interview at least 923 people in order to achieve a 90% confidence level with a sample mean within 11 minutes of the population mean. Since the sample size must be a whole number, you would need to round up to the nearest whole number. Therefore, you should interview at least 923 people.