Question

Five years ago, a survey found that the proportion of city employees who commute to work by car is 8%. A local city commissioner claims that the percentage is higher than it was five years ago. Data on employee commuting by car was collected on a random sample of 1000 employees and found 12% of employees commute by car. Test an appropriate hypothesis and state your conclusion at the 10% level of significance.

Answer 1

The data shows a proportion in car commuting greater than 8%

Explanation:

Five years ago, a survey found that the proportion of city employees who commute to work by car is 8%.

Claim : . A local city commissioner claims that the percentage is higher than it was five years ago.

`H_0:p=0.08\\H_a:p>0.08`

A random sample of 1000 employees was collected

n = 1000

They found 12% of employees commute by car.

No. of employees commute by car =
`(12)/(100) * 1000=120`

We will use one sample proportion test

x= 120

n = 1000

`\widehat{p}=(x)/(n)`

`\widehat{p}=(120)/(1000)`

`\widehat{p}=0.12`

Formula of test statistic =
`\frac{\widehat{p}-p}{\sqrt{(p(1-p))/(n)}}`

=
`\frac{0.12-0.08}{\sqrt{(0.08(1-0.08))/(1000)}}`

=
`4.66`

Significance level = 10%

α=0.1

`Z_(0.10)=1.28`(Using z table)

So, test statistic i.e.Z calculated > Z critical

So, we failed to accept null hypothesis .The data shows a proportion in car commuting greater than 8%