To determine whether owning a car affects a student's academic performance, two random samples of 100 male students were taken. The grade point average for the n1 = 100 non-car owners had an average and variance equal to 2.70 and 0.36 respectively. For the n2 = 100 car owners, they had a mean and variance equal to 2.54 and 0.40 respectively. Do the data present enough evidence to indicate a difference in the mean in performance between car owners and non-owners? Try using α = 0.05. Construct a 95% confidence interval for the difference in average academic performance between car owners and non-owners. Using the confidence interval, can it be concluded that there is a difference in the population means for the two groups of students?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
To determine whether owning a car affects a student's academic performance, two random samples of 100 male students were taken. The grade point average for the n1 = 100 non-car owners had an average and variance equal to 2.70 and 0.36 respectively. For the n2 = 100 car owners, they had a
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