Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is $55.4 thousand. A random sample of 90 classroom teachers in Ohio yielded the annual salaries, in thousands of dollars, presented on theWeissStats site. Use the technology of your choice to perform the following tasks. a. Obtain a normal probability plot, boxplot, histogram, and stemand-leaf diagram of the data. b. Based on your results from part (a), can you reasonably apply the one-mean z-test to the data? Explain your reasoning. c. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean annual salary of classroom teachers in Ohio is greater than the national mean? Assume that the standard deviation of annual salaries for all classroom teachers in Ohio is $9.2 thousand.
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!
Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The
a. Obtain a normal
b. Based on your results from part (a), can you reasonably apply the one-mean z-test to the data? Explain your reasoning.
c. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean annual salary of classroom teachers in Ohio is greater than the national mean? Assume that the standard deviation of annual salaries for all classroom teachers in Ohio is $9.2 thousand.
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