5. There are many complaints from passengers about the late running of buses on a particular route. The bus company claims that the proportion of buses that are delayed is 0.1. A passenger conducts a survey of a random sample of 200 buses and finds that 27 are delayed. Test, at the 5% significance level whether the proportion of buses that are delayed is more than that claimed by bus company.
Solution :
This is the right tailed test .
The null and alternative hypothesis is
H0 : p = 0.1
Ha : p > 0.1
= x / n = 27/200 = 0.135
P0 = 0.10
1 - P0 = 1 -0.10 = 0.90
Test statistic = z
= - P0 / [P0 * (1 - P0 ) / n]
=0.135 -0.10 / [0.10*(0.90) /200 ]
= 1.650
P(z > 1.650 ) = 1 - P(z < 1.650) = 0.0495
P-value = 0.0495
= 0.05
0.0495< 0.05
Reject the null hypothesis .
There is sufficient evidence to suggest that the proportion of buses that are delayed is more than that claimed by bus company
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