Question

4. In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 33.2 mpg with a standard deviation of 2.5 mpg, with the mileages approximately normally distributed.

H0 : µ = 33.2

Ha : µ < 33.2

Part a: Describe a Type II error in the context of the hypothesis test.

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 α = 0.05?

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

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...

In a recent publication, it was reported that the average
highway gas mileage of tested models of a new car was 34.2
mpg with a standard deviation of 1.5 mpg, with the mileages
approximately normally distributed.
H0 : μ = 34.2
Ha : μ < 34.2
Part a: Describe a Type II error in the context of the hypothesis
test.
Part b: If a simple random sample of 100 cars is selected, what
values of the sample mean ̄x would...

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highway mpg = 6.785 + (1.033 × city mpg)
for predicting highway mileage from city mileage.
(a) What is the slope of this line? (Enter your answer to three
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____mpg
Say in words what the numerical value of the slope tells us....

We expect a car's highway gas mileage to be related to its city
gas mileage (in miles per gallon, mpg). Data for all 1137 vehicles
in the government's Fuel Economy Guide give the regression
line
highway mpg = 6.785 + (1.033 * city mpg)
for predicting highway mileage from city mileage.
(a) What is the slope of this line? (Enter your answer to three
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mpg
Say in words what the numerical value of the slope tells us.
Highway...

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A car company claims that its cars achieve an average gas
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x overbarxequals=19.9
mpg and
s=6.8
mpg. Based on these sample data, compute and interpret a
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5. A consumer watchdog group tests the
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This sample
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[8 pts]
(b) Complete each step below to
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in bold made by...

A consumer agency claims that the average fuel mileage of Sedan
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