I am training a little on Hypothesis Testing, but unfortunately I was stuck on this issue. And the book I am studying has not explained well the part about what is asked for. I tried in several ways to reach the result but unfortunately without success. If anyone can help me I will be very grateful
It is known that the time needed to travel a given route in the late afternoon
can be studied by a Normal model. Sensors have been installed to control the
opening time of traffic lights present on the route and you want to check whether the time spent
to complete the route decreased. With the sensors deactivated, 11 vehicles of the same
year and brand called Group Control, had the time spent on the journey noted.
Then, the sensors were activated and 13 other vehicles (Test Group) also from
same year and brand followed the same route. Observed times, in minutes,
were
Control 38 26 20 70 16 26 38 32 45 49 32
Test 17 31 28 21 50 21 20 51 10 22 18 35 29
a) Use the Equality of Variance test to check whether the time variances are
equal at a significance level of 5%.
b) About the result of item a), check if the use of the sensors contributes to the decrease
tion of the average time spent in carrying out the route through a test of
hypotheses. Use a 5% significance level.
Answers:
Test to verify that the variances are equal: Test statistic: F = 1.53
Critical region: CR = {F ≤ 0.27 or F≥ 3.37}
Test for the hypothesis of interest: Test statistics: T = 195.53
Critical region: CR = {T> 1.71}
It is known that the time needed to travel a given route in the late afternoon
can be studied by a Normal model. Sensors have been installed to control the
opening time of traffic lights present on the route and you want to check whether the time spent
to complete the route decreased. With the sensors deactivated, 11 vehicles of the same
year and brand called Group Control, had the time spent on the journey noted.
Then, the sensors were activated and 13 other vehicles (Test Group) also from
same year and brand followed the same route. Observed times, in minutes,
were
Control 38 26 20 70 16 26 38 32 45 49 32
Test 17 31 28 21 50 21 20 51 10 22 18 35 29
a) Use the Equality of Variance test to check whether the time variances are
equal at a significance level of 5%.
b) About the result of item a), check if the use of the sensors contributes to the decrease
tion of the average time spent in carrying out the route through a test of
hypotheses. Use a 5% significance level.
Answers:
Test to verify that the variances are equal: Test statistic: F = 1.53
Critical region: CR = {F ≤ 0.27 or F≥ 3.37}
Test for the hypothesis of interest: Test statistics: T = 195.53
Critical region: CR = {T> 1.71}