Question

) 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.

a) Estimate the mean of all kids (ages 6-11) in Barcelona, using 99% confidence interval. (show all the calculations)

b) Write the conclusion of your result

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 28

sample standard deviation = s = 5

sample size = n = 100

Degrees of freedom = df = n - 1 = 100 -1 =99

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

t/2,df = t0.005,99 = 2.63

t /2,df = 2.63

Margin of error = E = t/2,df * (s /n)

= 2.63 * ( 5/ 100)

Margin of error = E = 1.31

The 99% confidence interval estimate of the population mean is,

- E < <  + E

28 -1.31 < < 28 + 1.31

26.69 < < 29.31

(26.69,29.31)

The kids watch the television during a typical week in Barcelona is 26.69 and 29.31 hours.