Question

A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 31 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was 58.1. Another random sample of 21 trucks were fitted with the old fuel injection system and driven under a variety of different conditions. For these trucks, the sample variance of gasoline consumption was 39.4. Test the claim that there is a difference in population variance of gasoline consumption for the two injection systems. Use a 5% level of significance. How could your test conclusion relate to the question regarding the consistency of fuel consumption for the two fuel injection systems?

(a) What is the level of significance?

State the null and alternate hypotheses. Ho: σ12 = σ22; H1: σ12 > σ22 Ho: σ12 > σ22; H1: σ12 = σ22 Ho: σ22 = σ12; H1: σ22 > σ12 Ho: σ12 = σ22; H1: σ12 ≠ σ22

(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)

What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent chi-square distributions.

We have random samples from each population.

The populations follow independent normal distributions.

The populations follow independent normal distributions. We have random samples from each population.

The populations follow dependent normal distributions.

We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. P-value > 0.200 0.100 < P-value < 0.200 0.050 < P-value < 0.100 0.020 < P-value < 0.050 0.002 < P-value < 0.020 P-value < 0.002 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence that the variance in consumption of gasoline is greater in the new fuel injection systems. Reject the null hypothesis, there is insufficient evidence that the variance in consumption of gasoline is greater in the new fuel injection systems. Reject the null hypothesis, there is sufficient evidence that the variance in consumption of gasoline is different in both fuel injection systems. Fail to reject the null hypothesis, there is insufficient evidence that the variance in consumption of gasoline is different in both fuel injection systems.

Answer #1

A new fuel injection system has been engineered for pickup
trucks. The new system and the old system both produce about the
same average miles per gallon. However, engineers question which
system (old or new) will give better consistency in fuel
consumption (miles per gallon) under a variety of driving
conditions. A random sample of 41 trucks were fitted with the new
fuel injection system and driven under different conditions. For
these trucks, the sample variance of gasoline consumption was...

A new fuel injection system has been engineered for pickup
trucks. The new system and the old system both produce about the
same average miles per gallon. However, engineers question which
system (old or new) will give better consistency in fuel
consumption (miles per gallon) under a variety of driving
conditions. A random sample of 41 trucks were fitted with the new
fuel injection system and driven under different conditions. For
these trucks, the sample variance of gasoline consumption was...

A new fuel injection system has been engineered for pickup
trucks. The new system and the old system both produce about the
same average miles per gallon. However, engineers question which
system (old or new) will give better consistency in fuel
consumption (miles per gallon) under a variety of driving
conditions. A random sample of 41 trucks were fitted with the new
fuel injection system and driven under different conditions. For
these trucks, the sample variance of gasoline consumption was...

A new fuel injection system has been engineered for pickup
trucks. The new system and the old system both produce about the
same average miles per gallon. However, engineers question which
system (old or new) will give better consistency in fuel
consumption (miles per gallon) under a variety of driving
conditions. A random sample of 31 trucks were fitted with the new
fuel injection system and driven under different conditions. For
these trucks, the sample variance of gasoline consumption was...

A new fuel injection system has been engineered for pickup
trucks. The new system and the old system both produce about the
same average miles per gallon. However, engineers question which
system (old or new) will give better consistency in fuel
consumption (miles per gallon) under a variety of driving
conditions. A random sample of 31 trucks were fitted with the new
fuel injection system and driven under different conditions. For
these trucks, the sample variance of gasoline consumption was...

Question 5. (Two Variances)A new fuel injection system has been
engineered for pickup trucks. The new system and the old system
both produce about the same average miles per gallon. However,
engineers question which system (old or new) will give better
consistency in fuel consumption (miles per gallon) under a variety
of driving conditions. A random sample of 31 trucks were fitted
with the new fuel injection system and driven under different
conditions. For these trucks, the sample variance of...

A new thermostat has been engineered for the frozen food cases
in large supermarkets. Both the old and new thermostats hold
temperatures at an average of 25°F. However, it is hoped that the
new thermostat might be more dependable in the sense that it will
hold temperatures closer to 25°F. One frozen food case was equipped
with the new thermostat, and a random sample of 26 temperature
readings gave a sample variance of 5.1. Another similar frozen food
case was...

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