Question

Now suppose we wish to conduct a hypothesis test to determine whether the standard deviation in highway mileage for all small cars is less than the standard deviation in highway mileage for all midsized cars produced in 2015. A sample of n1 = 47 small cars had a sample standard deviation of 4.533 HwyMPG while a sample of n3 = 34 midsized cars had a sample standard deviation of s2 = 4.785. Use this information to conduct the test at the 5% level of significance.

Answer 1

let 1 and 2 are population of small cars and midsized cars  

null hypothesis: Ho: ₁ =₂

alternate hypothesis:Ha: ₁ <₂

for (n1-1=47-1=46) and (n2-1=34-1=33) degree of freeedom in numerator and denominator with 0.05 level of significance rejection region F<0.592

here test statistic F =(s1/s2)² =(4.533/4.785)² =0.897

as test statstic is not in rejection region we can not reject null hypothesis

we do not have evidence at 0.05 level to conclude that standard deviation in highway mileage for all small cars is less than the standard deviation in highway mileage for all midsized cars produced in 2015.