Question

1. When hybrid vehicles were introduced the mean time required for savings from increased fuel economy to recover the additional initial cost was 4.2 years. To test whether it is now less an economist performed a study of 12 hybrid vehicles. The mean time cost recovery time was 3.9 years with sample standard deviation 0.6 years. The test is performed at the 1% level of significance. Assume that the population of recovery times is normally distributed. a) State the null and alternative hypotheses for the test. [2 points) b) State the formula for the test statistic and compute its value. Justify your answer. 4 points (c)Construct the rejection region and make a decision. 4 points] (d) State a conclusion about the mean recovery time of all hybrid vehicles, based on the test you performed. 12 points

Answer 1

Solution-

Appropriate hypotheses would be -

H₀ : $\mu$  $\geq$ 4.2

H_a : $\mu$ < 4.2

Sample mean is given to be $\overline{X}$ = 3.9 sample standard deviation (s) = 0.6 and sample size (n) = 12

then observed value of test statistic is equal to

Vn 7t

= -1.732

P-value will be calculated as P ( t₁₁ < -1.732 ) [ degree of freedom = 12- 1 = 11 ]

= 0.0556 ( using t tables )

We use t-distribution here as sample size is not large enough ( less than 30 ).

At 1% level of significance , we compare p-value and 0.01 ( It is a one- tailed test )

As p-value > 0.01 hence null hypothesis is rejected at 1% level of significance.

Thus we do not reject the null hypothesis and there is sufficient evidence that the mean recovery time is not less than 4.2 years.

TY!