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

Answer:

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

Step-by-step 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 = $\frac{12}{100} \times 1000=120$

We will use one sample proportion test  

x= 120

n = 1000

$\widehat{p}=\frac{x}{n}$

$\widehat{p}=\frac{120}{1000}$

$\widehat{p}=0.12$

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

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

                                       =$4.66$

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%