Question

An observational study using radar was conducted on a random selection of days on roadways where the posted speed limit is 50 mph. A random sample of 34 California drivers found they drove a mean speed of 55.5 mph and a standard deviation of 12.2 mph. Is there sufficient evidence at α = 0.10 significance level to determine if California drivers have a mean speed greater than 50 mph?

Answer 1

SOLUTION :

Given,

: California drivers

We formulate the null and alternative hypothesis is,

   50 Verses  

We are given that,

Number of California drivers ( n ) = 34,

Mean speed of drivers ( )=55.5 ,   

Standard deviation ( ) = 12.2

= 0.10 level of significance

The test statistic is,

Z = 2.6287...............( Calculated value )

   = 1.28........( From Z table )

Decision :

Z ( calculated Value ) > ( table value )

i.e. 2.6287 > 1.28 ( table value )

Reject null hypothesis at 10 % level of significance

Conclusion :

There is sufficient evidence to conclude that the California drivers have a mean speed greater than 50 mph.