Question

A leasing firm claims that the mean number of miles driven annually,

μ

, in its leased cars is less than

12620

miles. A random sample of

30

cars leased from this firm had a mean of

11399

annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is

2660

miles. Assume that the population is normally distributed. Is there support for the firm's claim at the

0.05

level of significance?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:
The value of the test statistic: (Round to at least three decimal places.)
The critical value at the 0.05 level of significance: (Round to at least three decimal places.)
Can we support the leasing firm's claim that the mean number of miles driven annually is less than 12620 miles?		Yes	or no

Answer 1

H0: 12620

Ha: < 12620

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 11399 - 12620 ) / ( 2660 / √( 30 ))
Z = -2.514
Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z(0.05) = 1.645
Z < -Z(α) = -2.514 < -1.645
Result :- Reject null hypothesis

Conclusion -

We have sufficient evidence to support the claim that the mean number of miles driven

annually is less than 12620 miles