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**Unformatted text preview: **"ﬂ \, STAT Z Midterm 2 ' a 1.“ You must use a Blue Book for this exam. It is OK to write on your exam paper, but
make sure everything that you want me to see when I grade your exam is in the blue
book. Show all work where appropriate. This exam has four problems followed by 10
True/False questions. There are 60 points possible, and the true/false questions are worth
a total of 20 points, so make sure to leave enough time to do them. There are 60points
possible on this exam. When you are ﬁnished, place this exam inside your blue book and
turn it in with your blue book. There is a copy of the Normal Distribution table at the end of this exam. The data for problems 2 and 4 can be found in the MINITAB file called EXAM2 in the data folder of the Peck folder on your desktop. 1. Suppose that the weights of bags of plain M&M's form an approximately normal distribution with a mean of 1.9 oz. and a standard deviation of .1 oz.
m; l D’ ': ' l (4) . A bag is under-filled if it weighs less than .84 oz. Approximately what . a
propan of bags are under-filled? ' . 84’ l .Ql \ V__
A ‘ \ a
(4) b. The lightest 10% of all bags of plain &M's weight less than what amount? 2. A maker of chocolate chip cookies claims an average of 30 chips per cookie. To test
this claim, 18 cookies are selected at random and the number of chips in each of the
selected cookies was recorded. The resulting data can be found in the column labeled CHIPS in the EXAM2 data
file. (2) a. Are there any outliers in this data set? (Use MINITAB to construct a boxplot. You DO NOT need to copy the boxplot onto your test paper or print it out--just use it to
determine if there are outliers).) (4) b. Based on looking at the boxplot of the data, is it reasonable to assume that the
population distribution of the variable x = number of chips is approximately normal?
Brieﬂy explain why or why not. (6) c. Is there sufficient evidence to conclude that the mean number of chips per cookie is less than the manufacturer's claim of 30? Test the appropriate hypotheses using
a = .05. ' 4;). low §%; ¥ 4. The 2 distribution for random samples of size 4 from a population with mean 40 STAT a Midterm 2
m 40 0?? The 5 distribution for random samples of size 4 from a population with mean 40
and standard deviation 8 will have a standard deviation of 4. and standard deviation 8 must be approximately normal. 5. The sample mean, 35 , will be within 2:7: of the true population mean for about
n 95% of all possible random samples. 6. If a 95% confidence interval for a population mean is reported to be (38, 47), this
means that the probability that u is between 38 and 47 is .95. 7. If a 99% confidence interval and a 90% confidence interval are both constructed using
the same set of data, the 99% conﬁdence interval will be wider. 8. Suppose that 15% of all those receiving a particular treatment improve after treatment.
Since each patient who receives the treatment either improves or does not, a reasonable
way of simulating an experiment where 3 patients are treated would be to use three random digits with the odd numbers representing improvement and the even numbers
representing no improvement. 9. In a hypothesis test, decreasing the probability of type I error increases the probability
of type 11 error. 10. An investigator collects data to determine if there is reason to believe that the mean
length of time required to solve a geometric puzzle is greater than 3 minutes. The appropriate hypotheses would be H 0 : [,1 > 3 vs. H a : ,u < 3. ...

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