The manufacturer of a sports car claims that the fuel injection system lasts ATLEAST 48 months before it needs to be rep

[answerhappygod]

The manufacturer of a sports car claims that the fuel injection
system lasts ATLEAST 48 months before it needs to be replaced. A
consumer group does NOT believe this claim.

The consumer group tests this claim by surveying a random sample of
15 sports car owners who had the fuel injection system replaced.
The ages of sports cars at the time of replacement were (in months)
as follows: Assume that that the age of sports cars at the time of
replacement is normally distributed.

29 42 49 48 53 46 30 51 42 52 38 47 50 34 52

a. . Find the sample mean and standard deviation of the above
sample data. (KEEP 2 DECIMALS )

SAMPLE MEAN =

SAMPLE STANDARD DEVIATION =


b. Construct a 99% confidence interval for the population mean
number of months a fuel injection system lasts before it needs
replacement. (KEEP 2 DECIMALS)

Lower Limit of the Confidence Interval =

Upper Limit of the Confidence Interval =


c. State the null and alternate hypotheses that would be used to
test the manufacturer's claim that the fuel injection system lasts
AT LEAST 48 months before it needs to be replaced.
H0: μ ≠ 48 and Ha: μ = 48H0: μ = 48 and Ha: μ >
48 H0: μ ≥ 48 and Ha: μ < 48H0: μ
< 48 and Ha: μ ≥ 48H0: μ ≤ 48 and Ha: μ > 48
d. Continuing part (c), find the p-value of the appropriate test
and decide whether or not to reject the null hypothesis at the 1%
significance level.

P-Value ( KEEP 3 DECIMALS) =

Conclusion At 1% level of Significance:
Do not reject the null hypothesis because the p-value is larger
than
𝛼. Conclude that the fuel injection system lasts ATLEAST 48
months before it needs to be replaced. Do not Reject the null
hypothesis because the p-value is less than
b. Conclude that the fuel injection system lasts ATLEAST 48
months before it needs to be
replaced. Reject the null hypothesis because
the p-value is less than
c. Conclude that the fuel injection system lasts less than 48
months before it needs to be replaced. Reject the null hypothesis
because the p-value is greater than
d. Conclude that the fuel injection system lasts less than 48
months before it needs to be replaced.
e. Does the manufacturers claim appear to be plausible? That is,
did you find sufficient sample evidence to support the
manufacturers claim?
NO. We do not have evidence to support the manufacturer's claim
since we rejected the null hypothesis.
YES. We have evidence to support the manufacturer's claim since
we did not reject the null hypothesis
f. What type of error is possible with your final decision about
the null hypothesis in part (d).
TYPE II ERROR
TYPE I ERROR