Question 1: A sample of the various prices for a particular product has been conducted in 16 stores which were selected at random in a neighbourhood of a city. The following prices were noted:
95, 108, 97, 112, 99, 106, 105, 100, 99, 98, 104, 110, 107, 111, 103, 110.
Assuming that the prices of this product follow a normal law of variance of 25 and an unknown mean:
a. What is the distribution of the sample mean?
b. Determine the confidence interval at 95% for the population mean.
Question 2: The average heights of a random sample of 400 people from a city is 1.75 m. It is known that the heights of the population are random variables that follow a normal distribution with a variance of 0.16.
a. Determine the interval of 95% confidence for the average heights of the population.
b. With a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of the heights to be less than 2 cm from the sample mean?
Question 3: Read the attached articles and search for at least 3 more references to design and implement a study to find which ball bounces best out of a Tennis ball, sponge ball, table tennis ball, roll-on ball, and a golf ball. The variables to be taken into account are the size of the ball, material, mass, density, compressibility, rigidity of the floor etc. By way of suggestion:
a. You could make changes to the temperature of each ball to test whether it affects the ball's ability to bounce.
b. You could change the type of surface the balls bounces on.
Ensure that you work with one other student to design and implement this experiment.