Answer:
The t value for 99% CI for 21 df is 2.831.
The critical value that should be used in constructing the confidence interval is (64.593, 86.407).
Step-by-step explanation:
Now the sample size is less than 30 and also population standard deviation is not known.
Then we will use t distribution to find CI
t value for 99% CI for 21 df is TINV(0.01,21)=2.831
The margin of error is
Hence CI is
a)
The average speed is equal to the ratio between the total distance ( and the total time taken (
):
the distance travelled by the trucker in the first 3 hour can be written as the time multiplied by the velocity:
So the total distance is
The total time is equal to the first 3 hours + the time taken to cover the following 20 miles in the city:
So, the equation can be rewritten as:
b) 0.50 h (half a hour)
Since we know the value of the average speed, , we can substitute it into the previous equation to find the value of
, the time the trucker drove in the city: