Problem 3: Suppose we want to estimate the average height of buildings in a city using the

number of floors as an auxiliary variable. We have the following data

Buildings 1 2 3 4 5

Number of floors 10 28 7 15 17

Height (in metre) 52 134 37 70 81

Assume that the average number of floors of buildings in this city is 18 and the number of

buildings is very large.

1. Estimate the average height of buildings in a city using regression estimation. Compute its

standard error.

2. Construct the 95% confidence interval for the average height of buildings in this city.

Problem 4: Suppose we want to estimate the average number of times a middle-age adult in a

town shopped online last week. However, we don't have a list of middle-age adults of this town.

A simple random sampling of 100 persons is taken and only 57 out of 100 persons are middle-age

adults. The following table summarizes the number of times these 57 middle-age adults shopped

online last week:

Number of times shopping online 0 1 2 3 4 5 6 7

Number of middle-age adults 17 20 10 6 3 0 0 1

Assume that the population of this town is much larger than 100.

1. Compute the estimate and its standard error.

2. Construct a 95% confidence interval for the average number of times a middle-age adult

shopped online last week.

3. Further assume that this town has a population of 10,000. Estimate the total number of times

all middle-age adults in this town shopped online last week. Construct a 95% confidence

interval for this quantity.

Please give the process of the answer thanks