Exam 3 Comments: 
A lot of spread!   Solutions outside my door, and on reserve.   Below 60's, please see me!
(May 9) total   #1 #2 #3#4 #5 #6 #7 #8 #9#10#11+5 10|1
possible 104    12  6 6 16  8 19  8 10  5 5  4  5  9|378
     max 101    12  6 6 16  8 19  8 10  5 5  4  5  8|225
      q3  82    12  6 6 16  8 13  7 10  5 2  3  5  7|044468
     med  74    12  4 6 12  8 11  6  8  5 2  2  5  6|4699
      q1  64.5  11  2 4  8  5  8  6  6  0 0  1  5  5|1
     min   5    6   1 3  0  0  3  3  0  0 0  0  5  4|067      

Hardest thing--fundamental understanding of meaning of confidence interval and significance test.
Many people don't have the mechanics under control.   If not, please see me Clinic or someone!
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#10) Find z* for 88% CI:   Meant to put into practice the picture you memorized for the quiz.    C is 88%.  To use the z table, you have to figure out what's in the tail(s).  1-.88 = .12  Divide by 2, find 6% in each tail.
88%+6% = 94% to the left of +z*.  Use the table backward, closest is .9394, for z* = 1.55
or .9406 for z*=1.56 (or z*=1.555, halfway between).

I also gave part credit if you told me it was between the values for 80% and 90%. A few people interpolated in the t-table, finding the number 8/10 of the way between the values for 80% and 90% (8/10 of the way between 1.282 to 1.645).  .  This is not quite right, since it's assuming the normal curve is flat in this region, (equal intervals contribute equal area) but numerically it comes out fairly close.
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4a, b)  This is patterned on 1 bottle of cola vs. 6, 1 test on Julie vs. 3 ( 4.51, 4.52) Another of that type is 4.43, p. 247.  Making the comparison between measuring one  individual from the population (a sample of size 1, or just the 'distribution of the population')  and measuring the mean from a sample of size n.  The distribution of the means will have less spread.
4c)  The probability that the sum of the 36 people's baggage is greater than 36x60 is the same as the probability that the average is greater than 60, because the average is the sum divided by 36.  (This was the "bonus points" problem; I was pleased that as many people got it as did.)
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6b) (answer =) Fish caught must be or act like a Simple Random Sample from the population.  All our formulas depend on that.  Part credit for sample must be representative of the population, no biases in the sampling.
Notice, the Sample may well not look normal.  If the Population isn't normally distributed, the Sample won't look normal either.

6c)  (answer = ) Central Limit Theorem is the Central theorem of classical statistics--it guarantees that for a large(ish) n and a Simple Random Sample of size n, the sampling distribution of the (sample) mean is approximately Normal.  This allows us to use the normal tables (and the t-tables too).
(part credit for) The Law of Large Numbers says that for large n (and again, a SRS), the sample mean will be close to the population mean.  But doesn't say anything about the distribution of sample means.

6d)  You can make a narrower confidence interval  (make a smaller margin of error) by
     i) taking a larger sample size (the sqrt(n) in the denominator will be bigger, make margin of error smaller)
 or iii) require lower confidence level (z* will be smaller, closer to the middle).
Higher confidence level <--> lower accuracy
  <--> wider interval<--> larger margin of error.
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11)  Voluntary Response Sample--almost sure to be biased.  Need Simple Random Sample or reasonable facsimile to do confidence interval, or any sort of inference.
(Or you need some sort of Probability Sample--maybe a more sophisticated one and a different formula.)

The size of the sample compared to the population of voters is not a problem.  A spoonful of soup gives just as good a sample of a huge pot of soup as it does of a small pot.  A toothpick full of soup, however, is not a good sample.  So the size of the sample per se is important, but the proportion of the population it represents is not.  Here the sample size is very large. 
(Qualification:  If you actually can sample a large part of the population, more than about 10%, you will get even stronger results than our formulas give.  There is a formula--"the finite population correction"--for adjusting the standard deviation of the sample mean when this is true.  P. 569, Ch.4 footnote 3.)

If you (correctly) said that the results can only describe the people who sent in answers, then you should notice that you already have  all of the population you are describing.  So your sample mean can't have any variability; it's just the mean of all the numbers you are hoping to describe.  So putting a margin of error around it doesn't make any sense.  


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