Question

# 5. There are many complaints from passengers about the late running of buses on a particular...

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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