Find the confidence interval:

Question

How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4 inches long and 1.5 inches square? Here are data from students doing a laboratory exercise:

33,190    31,860    32,590    26,520    33,280

32,320    33,020    32,030    30,460    32,700

23,040    30,930    32,720    33,650    32,340

24,050    30,170    31,300    28,730    31,920

Suppose that the strength of pieces of wood like these follows a Normal distribution with standard deviation of 3000 pounds. Give a 96% confidence interval for the mean load required to pull the wood apart.

[_______ to _______ ]

Answer 1

To find confidence intervals, we need to know a couple things. Firstly, what is the mean? To get the mean we add up all the data points and divide that total by the number of observations. In this case μ=30841.

Then we need to know the standard deviation, which is given in our problem at 3000 lbs.

Finally, we need to make sure that we are using a normal distrobution, there are lots of distrobutions, so we need to be careful here. Since the distrobution is normal, we can go ahead and apply our equations for z scores and confidence intervals!

Using a table (likely locaated in the back of your textbook), we can look up what value of z is equivilent to a a percentage of 98%. we use 98% because this is a two tailed interval. we have 2 percent on the right and left hand sides of the distrabution missing, so in total. 96% will be in the middle. The z score we get is 2.06..

The z score tells us how many standard deviations we need to go above and below the mean to get to that 96% in the middle of our normal distrobution.

From there we have CI= 30841 +(-) 3000*2.06.

So a 96% confidence interval for this problem is from 24661 to 37021