Answer:
t = 2.9272 > 1.708 at 25 degrees of freedom
null hypothesis is rejected
The council decides that it will increase the transportation budget if the amount of waiting time for drivers is not exceeds 18 minutes
Step-by-step explanation:
<u>Step (i):</u>-
A sample of 26 main roads results in a mean waiting time of 21.1 minutes with a sample standard deviation of 5.4 minutes.
Given sample size 'n' = 26
The mean of the sample 'x⁻ = 21.1 min
Standard deviation of the sample 'S' = 5.4 min
The Population mean 'μ' = 18min
<u>Step(ii)</u>:-
<u>Null hypothesis: H₀</u> : The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 18 minutes.
'μ' > 18min
<u>Alternative hypothesis</u> :H₁:
'μ' <18min
<u>Level of significance :</u> ∝=0.05
Degrees of freedom γ = n-1 = 26-1 =25
The test statistic
t = 2.9272
<u>Step(iii)</u>:-
The tabulated value t = 1.708 at 25 degrees of freedom
t = 2.9272 > 1.708 at 25 degrees of freedom
Null hypothesis is rejected at 5% significance level of significance
<u>Conclusion</u>:-
The council decides that it will increase the transportation budget if the amount of waiting time for drivers is not exceeds 18 minutes