. A manufacturer of a new car claims the typical car will average 33 mpg of gasoline. An independent consumer group is skeptical of the claim and thinks the mean gas mileage is significantly different than the 33 claimed. A sample of 50 randomly selected cars produced a mean mpg of 31 with a standard deviation of 3.5. Assume that cars’ gas mileage is normally distributed in the population. ). a. The manufactures want to determine if the mean mpg for the cars is significantly different from 33. Write the null and alternative hypotheses for this question. b. What are the assumptions of this test? Are the assumptions met? ). C. Calculate and interpret the 95% confidence interval, and assess whether to reject the null hypothesis based on the interval. Use a t critical of 2.01.
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 + ...
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
