Question

The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of the cars at the time of replacement were (in months):

23 46 41 48 53 46 30 51 42 52

(i) Use your calculator to calculate the mean age of a car when
the fuel injection system fails *x* and standard deviation
*s*. (Round your answers to two decimal places.)

x̅ = _____ months

s=_____ months

(ii) Test the claim that the fuel injection system lasts less than
an average of 48 months before needing replacement. Use a 5% level
of significance.

What are we testing in this problem?

**A.)** single proportion

**B.)** single
mean

(a) What is the level of significance?

State the null and alternate hypotheses.

**A.)**H_{0}: μ = 48;
*H*_{1}: μ ≠ 48

**B.)***H*_{0}: μ = 48;
*H*_{1}: μ <
48

**C.)***H*_{0}: μ = 48;
*H*_{1}: μ > 48

**D.)**H_{0}: *p* = 48;
*H*_{1}: *p* ≠ 48

**E.)** *H*_{0}: *p* = 48;
*H*_{1}: *p* > 48

*H*_{0}: *p* = 48;
*H*_{1}: *p* < 48

(b) What sampling distribution will you use? What assumptions are
you making?

**A.)** The standard normal, since we assume that
*x* has a normal distribution with known σ.

**B.)**The Student's *t*, since we assume
that *x* has a normal distribution with unknown σ.

**C.)** The Student's *t*, since we assume
that *x* has a normal distribution with known σ.

What is the value of the sample test statistic? (Round your
answer to three decimal places.)

(c) Find (or estimate) the *P*-value.

**A.)** P-value > 0.250

**B.)** 0.125 < *P*-value < 0.250

**C.)** 0.050 < *P*-value < 0.125

**D.)** 0.025 < *P*-value < 0.050

**E.)** 0.005 < *P*-value < 0.025

**F.)** *P*-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis? Are the data statistically
significant at level α?

**A.)**At the α = 0.05 level, we reject the null
hypothesis and conclude the data are statistically significant

**B.)** At the α = 0.05 level, we reject the null
hypothesis and conclude the data are not statistically
significant.

**C.)** At the α = 0.05 level, we fail to reject
the null hypothesis and conclude the data are statistically
significant.

**D.)** At the α = 0.05 level, we fail to reject
the null hypothesis and conclude the data are not statistically
significant.

(e) Interpret your conclusion in the context of the
application.

A.) There is sufficient evidence at the 0.05 level to conclude that the injection system lasts less than an average of 48 months.

**B.)** There is insufficient evidence at the 0.05
level to conclude that the injection system lasts less than an
average of 48 months.

Answer #1

The manufacturer of a sports car claims that the fuel injection
system lasts 48 months before it needs to be replaced. A consumer
group tests this claim by surveying a random sample of 10 owners
who had the fuel injection system replaced.
The ages of the cars at the time of replacement were (in
months): 23 42 49 48 53 46 30 51 42 52
Use the sample data to calculate the mean age of a car when the
fuel...

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...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 19 minutes ago

asked 28 minutes ago

asked 32 minutes ago

asked 35 minutes ago

asked 54 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago