6.An insurance company wants to know if the average speed at which men drive car

Question

6.An insurance company wants to know if the average speed at which men drive cars is great than that of women drivers. The company took a random sample of 27 cars driven by men on a highway and found the mean speed to be 72 miles per hour with a sample standard deviation of 2.2 miles per hour. Another sample of 18 cars driven by women on the same highway gave a mean speed of 68 miles per hour with a sample standard deviation of 2.5 miles per hour.

6.1 Construct a 95% confidence interval for the difference between the mean speeds of cars driven by all men and all women on this highway.

6.2 Test at the 2% significance level whether the mean speed of cars driven by all men drivers on this highway is greater than that of cars driven by all women drivers.

Explanation / Answer

x1 =72 ; s1=2.2 ;n1=27

x2=68 ; s2=2.5 ; n2=18

here degree of freedom =((s12/n1+s22/n2)2/((s12/n1)2/(n1-1)+(s22/n2)2/(n2-1)) =33

here std error =(s12/n1+s22/n2)1/2 =0.7069

for 95% CI, for 33 degree of freedom ; value of t =2.0345

hence confidence interval =(x1-x2) +/- t*std error =2.5617 ; 5.4383

6.2) for test stat =(x1-x2)/std error =5.658

fro which p value =0.0000

as p value is less we reject null null hypothesis; that both mean are equal, and conclude that mean speed of cars driven by all men drivers on this highway is greater than that of cars driven by all women drivers.

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