OK, so I am preparing for a statistics quiz tomorrow and I ran across a problem I should know how to work, but now I am stuck on. “Corssett Truck Rental has a large fleet of rental trucks. At times many of the trucks need substantial repairs. Mr. Crossett has requested a study of the repair costs. A random sample of 64 trucks is selected. The mean annual repair cost is 1200, with a standard deviation of 280. Estimated the mean annual repair cost for all rental trucks. Develop the 95 percent confidence interval for the population mean.” Now I don’t want just the answer to this problem and no, it’s not homework. I realize the first thing I have to do for this problem is first calculate the z value. I thought that I was to take the 1200-64 and take that answer and divide by 280, but I must be wrong, since it says that z value is 1.96 and that is the not the answer the above method yields. With this being said, am I using the right numbers or do I need to calculate some other ones first? Thanks.
The answer can be found here:
To answer your question directly, the z-value is a value in standard deviations (where the mean is 0 and the standard deviation is 1). It just so happens that the 95% confidence interval corresponds to a z-value of 1.95. You can find this by looking at certain charts. If you have a stats book, this would be in a chart at the back of the book.
So wouldn’t that make it 1.95 instead of 1.96?
ok, I think I figured it out. What I should do is take 95% of .5 because that’s half of the range. Take that answer and find it in the chart labeled area under the normal curve and that will give me my answer.