Question

1. For an effective parental skill study, a researcher asked: How many hours do your kids watch the television during a typical week in Barcelona? The mean of 100 Kids (ages 6-11) spend about 28 hours a week in front of the TV. Suppose the study follows a normal distribution with standard deviation 5.

1. Estimate the mean of all kids (ages 6-11) in Barcelona, using 99% confidence interval. (show all the calculations)
2. Write the conclusion of your result

Answer 1

Part a

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 28

σ = 5

n = 100

Confidence level = 99%

Critical Z value = 2.5758

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 28 ± 2.5758*5/sqrt(100)

Confidence interval = 28 ± 1.2879

Lower limit = 28 - 1.2879 = 26.71

Upper limit = 28 + 1.2879 = 29.29

Confidence interval = (26.71, 29.29)

Part b

We are 99% confident that the average mean time in hours for all kids’ watch the television will lies between 26.71 hours and 29.29 hours.