CIV2235—STRUCTURAL MATERIALS
Week 11 Practice Class
Statistical Testing
Question 1 [40 marks]. The average adult male height in a certain country is 170 cm. We suspect that the men in a certain city in that country might have a different average height due to some environmental factors. We pick a random sample of size 9 from the adult males in the city and obtain the following values for their heights (in cm):
176.2 157.9 160.1 180.9 165.1 167.2 162.9 155.7 166.2
Assume that the height distribution in this population is normally distributed. Here, we need to decide between H0: μ = 170, H1: μ ≠ 170. Based on the observed data, is there enough evidence to reject H0 at significance level α=0.05?
Question 2 [30 marks]. A survey in a specific suburb leads to the conclusion that the residents drive their cars, on average, 256 kilometres per week. One resident wants to find out if this average is also valid for himself. For 21 weeks he keeps track of the number of kilometres he drives. The average and standard deviation turn out to be 302.4 and 38.0 km, respectively.
With a confidence of 0.8, can the resident claim that he drives a different amount of kilometres per week than the average driver in his suburb?
Question 3 [30 marks]. A shop in a shopping mall has been receiving on average 102 clients per day for the last few years. A new employee claims that she can increase this average by using a new advertising strategy. The shop owners allow her to test this. After 24 days with the new strategy, the number of customers served per day is 103.0, with a calculated standard deviation of 7.0.
With a confidence of 0.85, can the employee claim that she increased the amount of customers?
Practice (no mark). As a part of her evaluation of municipal employees, the city manager audits the parking tickets issued by city parking officers to determine the number of tickets that were contested by the car owner and found to be improperly issued. In past years, the number of improperly issued tickets per officer had a normal distribution with mean of 380 and standard deviation of 35.2.
Because there has recently been a change in the city’s parking regulations, the city manager suspects that the mean number of improperly issued tickets has increased. An audit of 50 randomly selected officers is conducted to test whether there has been an increase in improper tickets. Use the sample data (n = 50 and the mean number of improperly issued tickets is 390) and α = 0.01 to test the research hypothesis that the mean number of improperly issued tickets is greater than 380.