[1]. The manufacturer of a new model car claims that a typical car gets 26 miles

Question

[1]. The manufacturer of a new model car claims that a typical car gets 26 miles per gallon (mpg). A consumer advocacy group, however, is skeptical of this claim and thinks that the mean gas mileage, , of the new model cars is not what the manufacturer claims to be. The consumer advocacy group plans to randomly test mpg (a) (10 points) Is there any evidence to believe the claim of the manufacturer? (b) (10 points) Find the probability of making a type ll error if the true mean gas Show your calculations for credit. mileage of all the new model cars is 25.8 mpg.

Explanation / Answer

a)
Below are the null and alternate hypothesis
H0: mu = 26
H1: mu < 26

As sample mean is not given, we assume it to 24.7 (Note if this value is different let me know, I will solve this again)

test statistics, t = (24.7 - 26)/(1.4/sqrt(30)) = -5.086

p-value = 0.00000 (<0.05)

Hence we reject the null hypothesis. This means there are significanct evidence to conclude that a new model car has mileage different than 26 mpg.

b)

mu0 (hypothesised mean) 26 sigma 1.4 n 30 alpha 0.05 sample/true mean 25.8 Std. Error. SE = sigma/sqrt(n) 0.2556 Zcritical -1.960 Xcritical values 25.50 Beta or type II error is the probability of fail to reject the null hypothesis P(X<25.5|mu=25.8) 0.11950 Hence type II error probability is 0.1195 Power of the test 0.8805

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