The speed limit on College Terrace is 25 mph. Even after traffic-calming measures, a resident complains that cars still speed. 250 randomly selected cars were clocked with mean speed 25.55 mph and a standard deviation of 3.618. Is the mean speed of all cars greater than 25 mph? Use a significance level of ? = 0.05.a) Write the hypotheses. b) Perform the appropriate hypothesis test using a significance level of ? = 0.05, report the test statistic and p-value, and write a full conclusion. Be sure to write out what you entered in your calculator.c) Are the results statistically significant? Why or why not?d) Find the appropriate 90% confidence interval. Be sure to write out what you entered in your calculator. e) Are the results practically significant? Why or why not?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...