Question

In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 33.2 mpg and approximately normally distributed. A consumer group conducts its own tests on a simple random sample of 17 cars of this model and finds that the mean gas mileage for their vehicles is 31.5 mpg with a standard deviation of 3.5 mpg. Perform a test at the level to determine if these data support the contention that the true mean gas mileage of this model of car is different from the published value.

Ho: M=33.2 Ha: M<33.2

part b: If a simple random sample of 100 cars is selected, what values of the sample mean x would represent sufficient evidence to reject the null hypothesis at significance level =.05

part c: If the actual population average gas mileage is 32.8 mpg, determine the probability that the null hypothesis will be rejected if a simple random sample of 100 cars is selected

part d: If the sample size were greater than 100 cars, what would happen to the probability in part c? explain your reasoning

Answer 1

given that

sample size=n=17

sample mean =m=31.5

Sample SD=S=3.5

we have to test that

a)

test statistics is given by

t have DF=n-1=17-1=16

P Value =P(t<-2.00)=0.03

since P value is less than level of significance (0.05) hence we reject H0

b)

Here n=100

so we will use Z test

now for alpha =0.05

we reject H0 if sample mean < critical value

critical value is given by

P(Z<critical value)=0.05

from Z table

P(Z<-1.645)=0.05 hence

critical value =-1.645

now

we reject H0 if m<32.62

c)

now

d)

since

as "n" increase then value

will become less negative hence probability will increase.