Question

In a sample of 50 households, the mean number of hours spent on social networking sites during the month of January was 45 hours. In a much larger study, the standard deviation was determined to be 8 hours. Assume the population standard deviation is the same. Which of the statement below best describes that there is a 95% confidence interval for the mean hours devoted to social networking in January? A. The 95% confidence interval ranges from 8 to 45 hours. B. The 95% confidence interval ranges from 40.13 to 45.78 hours. C. The 95% confidence interval ranges from 43.87 to 46.13 hours. D. The 95% confidence interval ranges from 42.78 to 47.22 hours.

Answer 1

Answer:

D. The 95% confidence interval ranges from 42.78 to 47.22 hours.

Step-by-step explanation:

In a sample of 50 households, the mean number of hours spent on social networking sites during the month of January was 45 hours. In a much larger study, the standard deviation was determined to be 8 hours.

Here,

n = sample size = 50,

μ = mean = 45,

σ = standard deviation = 8,

We know that, confidence interval will be,

$=\mu\ \pm\ z\dfrac{\sigma }{\sqrt{n}}$

For a confidence interval of 95%, we use z = 1.96, putting the values

$=45\ \pm\ 1.96\dfrac{8}{\sqrt{50}}$

$=42.78,47.22$

Answer 2

D. The 95% confidence interval ranges from 42.78 to 47.22 hours.

To solve the interval, we used the upper and lower limit formulas wherein:
xbar = 45
z = 1.96
s = 8
n = 50