does the evidence show that the cars are exceeding the posted speed limit? explain

Question

Are care exceeding the speed limit of 40mpg? a resident took a simple random sample of 40 automobiles over a period of several days and constructed the confidence interval of (37.4mph, 44.3mph) at a 95% level of confidence.

Answer 1

Christina:

 

Reword the problem correctly.

 

Does the evidence show that the cars are exceeding the posted speed limit ON AN AVERAGE?

 

The resident measured what?  I think "speed of the 40 cars".  Assume that the speeds of cars in the population have a normal distribution, and with that assumption, a confidence interval for the average speed of cars in the population constructed. 

 

Since it is of interest to see whether or not the data have evidence for or against the statement that cars are exceeding the speed limit of 40 on an average, determine whether or not 40 is included in the confidence interval or not. If included, there is lack of sufficient evidence to say that average speed exceeds 40, at a certain confidence level.  If not included then there is enough evidence to say that the average speed exceeds 40, at a certain confidence level.

I

It is included.  So there is lack of sufficient evidence to say that average speed exceeds 40, at a certain level of significance.

 

Also, your interest is in whether or not the cars are exceeding on the average the speed limit of 40.  (If they do not then that is OK).   This one-sided-ness  changes the level of significance to  to 0.025.   [ 1 - 0.95 = 0.05. the changed  level of significance, due to one-sided-ness,  is 0.05/2 = 0.025]

 

So the conclusion:

 

There is not enough evidence in the data to conclude, at 2.5 per cent level of significance, that population average speed of cars  exceeds 40 mph, under the assumption that speeds of cars in the population have a normal distribution.