Question

the city of Chicago has for many years reported that the average distance from home to work for its employed residents is 12.60 miles. A researcher believes that the average is now shorter, and collects data on a random sample of 17 employed Chicagoans. In that sample, the mean distance to work was 10.25 miles, with a standard deviation of 3.62.

Using significance level .05, test these claims. Show all steps covered in class, including any notation used for the setup of the problem.

Answer 1

#here

null and alternative hypothesis is

H0:=12.60

ie   average distance from home to work for its employed residents is 12.60 miles.

Ha:12.60

ie   average distance from home to work for its employed residents is not equal to  12.60 miles.

Here

n=17

=10.25

s=3.62

#test statistics is

#test statistics is =-2.68

df=n-1=16

#P-value=P(|t16|>2.68)=0.01643

value t is obtain from t-table with corresponding degree of freedom =16

Decision rule:

#P-value<0.05 hence we reject the null hypothesis

Conclusion: hence reject Ho and conclude that average distance from home to work for its employed residents is not equal to  12.60 miles.