Assignment III
Sampling Distribution and Estimation
1.
The following data represent the number of days absent per year in a population of six employees of
a small company:
1
2.
3
6
7
9
10
a.
Assuming that you sample without replacement, select all possible samples of n = 2 and
construct the sampling distribution of the mean. Compute the mean of all the sample means
and also compute the population mean. Are they equal? What is this property called?
b.
Compute the standard deviation of the population? Compute the standard deviation of
sampling distribution in (a). What is it called? How can you find that value from the population
standard deviation?
A market researcher for a consumer electronics company wants to study the media viewing
behaviour of residents of a particular area. A random sample of 40 respondents is selected, and each
respondent is instructed to keep a detailed record of time spent engaged viewing content across all
screens (Traditional TV, DVD/Blue-ray, game console, Internet on a computer, video on a computer,
video on a mobile phone) in a particular week. The results are as follows:
•
•
Content viewing time per week: 𝑋̅ = 41 ℎ𝑜𝑢𝑟𝑠, 𝑆 = 3.5 ℎ𝑜𝑢𝑟𝑠
30 respondents have high definition (HD) on at least one television set.
a.
Construct a 95% confidence interval estimate for mean content viewing time per week in this
area.
b.
Construct a 95% confidence interval estimate for the population proportion of residents who
have HD on at least one television set.
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