Explain the following concepts and using mathematical notation.

a) An unbiased estimator

b) A consistent estimator

c) A point estimator

d) An interval estimator

Section B: Confidence interval for one sample

2. In a random sample of 80 nails, the average weight was 1.56g. It is known that the weight

of this type of nails is normally distributed with a standard deviation of 0.1g.

a) Find a 95% confidence interval for the mean weight of this type of nail

b) Find a 99% confidence interval for the mean weight of this type of nail

c) What is the level of confidence level of the interval (1.54, 1.58)?

3. Temperature readings are taken on the same day of the year (1 January) over a ten year

period in a certain city. The data are displayed below. If we treat the data as a random

sample, obtain a 98% confidence interval for the mean temperature in this city on 1 January.

Assume the temperatures are normally distributed.

32 36 35 23 26

33 27 25 29 36

4. A survey is conducted with drivers in Cape Town to estimate what proportion use a seatbelt

regularly when driving. Of 800 people surveyed, 460 indicate that they use a seatbelt

regularly.

a) Give a point estimate and an interval estimate (with 95% confidence) for the proportion

of drivers who use a seatbelt regularly. For the interval estimate, use the t distribution

approach.

b) Repeat the interval estimate, this time using the Wilson score interval approach.

5. A politician hires a statistical consultant to conduct a poll to estimate the proportion of the

population who view him favourably. The poll consists of a random sample of 250 adults,

of whom 157 say they view the politician favourably.

a) Give a 90% confidence interval for the proportion of the population who view this

politician favourably. Use the t distribution approach.

b) Recalculate the 90% confidence interval using the Wilson score interval approach.