Answers to the Second Practice Midterm

1. A. First, you don't know anything about the population (except its UCLA male undergraduates). Second, use the information from the sample to construct a 99% confidence interval. Third, you will need the sample average and the SE for the average. 

SE for the average = SQRT(36) x 3
                     ------------ = .5
                           36
So a 99% confidence interval will be 69 inches plus or minus (3 x .5) where 3 is the positive Z score associated with 99% of the area under the curve. If you work out the range it is 67.5 to 70.5 inches

This is a Chapter 23 problem.

2. B. Here, you can tell that the average is going to be 18.3... but the trick is to calculate the SD of the sample which should be 8.1737. Then you will need the SE for the average for this sample: 

SE for the average = SQRT(10) x 8.1737
                     -----------------  = 2.58
                           10
I think I'll make this one a little bit harder... This is a Chapter 23 problem.

3. C

OK. You don't have any population information, so you use what you have, the 33% from the sample.

SE for the percentage = SQRT(1449) x SQRT(.67 x .33)
                        ----------------------------  x 100
                               1449
This is a Chapter 21 problem.

4. A

5. D. This should have been written better, but basically choice D is the best among what you have been given. This is a problem from Chapter 19.

6. D. I consider this one difficult. The "box" is the pumpkin patch and you know the parameter: 12lb average with a standard deviation of 2lbs. A single crate then is expected to weigh 192lbs which is the sum of 16 pumpkins. The trick is the standard error. It is: 

SE for the sum = SQRT(16) x 2 = 8
And so the Z statistic looks like: 
    195 - 192
Z = --------- = 3/8 = about .40
        8
Draw a picture...you want the area to right of 195 since the question asks for a crate weighing more than 195 pounds. This should be 34%

This is from Chapter 17.

7. C. Remember to use 100 instead of 121. There was a typo on this problem.

OK. If 15% is the true percentage, in a sample of 100 we would expect 15 people would say yes to the question "is Elvis Presley still alive" give or take some chance error. You are asked for the CHANCE that 10 or fewer say yes.

You will need the standard error for the number to calculate the chance. 

SE for the number  = SQRT(100) x SQRT(.85 x .15) = 3.57
So you'd expect 15 people give or take 3.57 people. So for the CHANCE of getting 10 or fewer people: 
10 -15
------ = about -1.40
  3.57
The area to the left of -1.40 is about 8%

This is Chapter 19/20.

8. A. The coin is fair, it doesn't really matter if it is not, because the question is asking about your understanding of how the SE of the sum works.

For 50 tosses, the SE of the sum is:

SQRT(50) x SQRT(.5 x .5) = 3.53

For 100 tosses, the SE of the sum is:

SQRT(100) x SQRT(.5 x .5) = 5

Chances are, if you must guess the exact number of heads that show up, you are more likely to be off the mark as the number of tosses go up.

Chapter 17

9. D. I probably should have written that you could assume that Fresno and San Diego were alike demographically. But even without that, given the choices before you, A and C are made out of thin air, no formulas like that exist.

B and E are trying to lead you down the relative size path which isn't right (see Chapter 20 p. 369). Sample accuracy depends on sample size, it really doesn't matter what the population looks like or how big it is. This is probably why they call this discpline "statistics" instead of "parameters". All that really matters is how you generate your statistics and whether they are accurate.

That leaves D.

10. D. This should be easy for you by now. What you will need to remember is how to calculate an average. The percentages give you the relative frequency of the delivery times. So it's like there are 5 delivery times of 10 minutes, 20 of 15 minutes and so forth. The calculation of the expected value for the average delivery time is (remember the expected value for the average is the same as the "box" average): 

(5 x 10) + ( 20 x 15) + (50 x 30) + (20 x 45) + (5 x 60)
-------------------------------------------------------- = 30.5
                100
so 30.5 minutes.  Another way you can do it is:


(.05 x 10) + (.20 x 15) + (.50 x 30) + (.20 x 45) +(.05x60) = 30.5
Calculate the box average in whichever manner is most comfortable for you, there isn't a right way, only a right answer. When you are confronted with unequal proportions (i.e. 5%, 20% etc) you've got to take the unequal distribution into account when calculating the average. In other words, just don't add 10+15+30+45+60 and divide by 5. You'd be giving them equal weighting and that's not the case.