Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 279 hybrid sedans and get a mean of 27 mpg with a standard deviation of 5.25 mpg. Also, 250 non-hybrid sedans get a mean of 26 mpg with a standard deviation of 6.25 mpg. Suppose that both populations are known to be normal distributed. Conduct a hypothesis test to evaluate the manufacturers' claim. Test at a 2% level of significance. Let population 1 denote non-hybrids and population 2 denote hybrids. (a) H0 : μ1 μ2 (b) Ha : μ1 μ2 (c) In words, state what your random variable represents. The random variable is the (mean/difference in mean/difference in the) miles per gallon of non-hybrid sedans and hybrid sedans. (D) What is the test statistic? Round your answer to three decimal places (E) What is the p-value? Round your answer to three decimal places. p-value = (F) Alpha: Decision: (reject/decline to reject) Reason for decision: p-value ( > or <_ ) α Conclusion: There (is/ is not) sufficient evidence to conclude that the mean miles per gallon of non-hybrid sedans is less than that of hybrid sedans.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 279 hybrid sedans and get a mean of 27 mpg with a standard deviation of 5.25 mpg. Also, 250 non-hybrid sedans get a mean of 26 mpg with a standard deviation of 6.25 mpg. Suppose that both populations are known to be normal distributed.

Conduct a hypothesis test to evaluate the manufacturers' claim. Test at a 2% level of significance.

Let population 1 denote non-hybrids and population 2 denote hybrids.

(a) H0 : μ1 μ2

(b) Ha : μ1 μ2

The random variable is the (mean/difference in mean/difference in the) miles per gallon of non-hybrid sedans and hybrid sedans.

(D) What is the test statistic?

Round your answer to three decimal places

(E) What is the p-value?

Round your answer to three decimal places.
p-value =

(F)

Alpha:
Decision: (reject/decline to reject)
Reason for decision: p-value ( > or <_ ) α
Conclusion: There (is/ is not) sufficient evidence to conclude that the mean miles per gallon of non-hybrid sedans is less than that of hybrid sedans.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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