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**Unformatted text preview: **/ ,p- stat 35000 Sample Final Exam Spring 2017 Your name:
__________________ ° Turn Off 3’0111' cell phone before the exam begins! ' Show YOUr work on all questions. Unsupported work may not receive full credit. ' REPOIt decimal answers to three decimal places. 0 -You are responsible for upholding IUPUI’s stande for academic integrity This
Includes protecting your work from the eyes of other students. 0 You are allowed the following aids: a. one-page (front and back) 8.5 x 11 handwritten
formula sheet, a scientiﬁc/graphing calculator, and pens/pencils. 0 When you are done, turn in both your exam and your formula. sheet. Points Possible Points Earned Problem
1. 3
follows mermaids-ﬂ: 4.+ 6 + 5 = 23) The lifetime of a. certain battery, denoted by X ,
are 49 ch 8 _n ““0“ With mean of 8 hours and standard deviation of 2 hour. There
su batteries in a package. 1. C . .
p122: Oilﬁnd the Probability that a battery will die within 10.5 hours? If you can,
e c culate the probability; if you can not, please explain why. 2. We are interested in the average lifetime of all batteries in a package, denoted by X. Specify name of the approximate distribution and parameter values for X. 3. What theorem did you use to obtain the above approximate distribution? Under
What condition can you use this theorem? 4. Find the 10th percentile of the X distribution. percentile you found in the previous step by X0. Suppose the
’5 customer service policy guarantees that any package of bat-
d an average lifetime of X0 hours will be replaced free of
And the policy also guarantees to pay $5 back to the cus- tomer if the average battery lifetime is longer than X0 hours but shorter than 8
$25 to replace a package of batteries (materials hours. It costs the manufacturer
plus mailing to customer). How much does the manufacturer expect to pay under this customer service policy? 5. Denote the 10th
battery manufacturer
teries that does not yiel
charge to the customer. Let X = number of ﬂaws on an electroplated Problem 2. (4+4+6+4+6 = 24)
the following PMF: automobile grill. Its distribution is modeled by a: 0 1 2 3
p(m 0.8 0.1 0.05 0.05 1. Wh -
at 18 the Probability that there are at most 1 ﬂaw on the Eli": i.e. P(X S 1)? 2' will Y be total number of grills with at most 1 ﬂaw in a random sample Of 100 grills.
at 18 the exact distribution of Y? Please specify name and parameter values for distribution of Y. 3. Find the probability that no grills from the sample Of 100 has at most 1 ﬂaw, using
the exact distribution. 4. What is the approximate distribution of Y? Please specify name and parameter
values for distribution of Y. 5. Find the probability that less than 85 grills have at most 1 ﬂaw, using the approx-
imate distribution of Y. Problem 3. (4 + 2 + 3 + 6 + 4 + 4 = 23) Newly manufactured automobile tires of a
certain type are supposed to be ﬁlled to a pressure of 34 psi. To avoid over-ﬁlling, the
manufacturer wants to perform a test on the average pressure ﬁlled. To do so, they take
a random sample of 36 tires whose average pressure is calculated to be 34.66 psi and
standard deviation is 2.53 psi. Assume that the tire pressures are normally distributed. 1. State the null and alternative hypotheses. 2- Wh
at dees the Parameter Ju in the hypotheses represent. 3. Which method Would you use?
(a) 1'531111318 T (b) 1-sample Z (c) 2-sample T (d) 2-sample Z 4. Calculate the test statistic and the P value. 5. State your conclusion in the context of the problem, i.e. Whether tires are over-ﬁlled on average. (assume a = 0.05) 6. Someone might argue that the above testing procedure (calculating a p-value, etc)
is unnecessary. Their reasoning goes as follows: the sample produced an average
pressure of 34.66 psi, which is higher than the standard pressure of 34 psi, so conclude that on average the tires are over-ﬁlled. Do you agree with this line of
reasoning? Explain. Problem 4. (4+2+3+6+4+4 = 23) Urban storm water can be contaminated by many
sources, including discarded batteries. When ruptured, these battries release metals of environmental signiﬁcance. The following are summary data on zinc mass (g) for two
different brands of size D batteries found in urban areas around Cleveland. We would like to decide whether on average the zinc mass is different for the 2 brands of batteries. Brand I Sample Size Mean SD. A 15 138.52 7.76
B 20 149.07 5.52 1. State the null and alternative hypotheses. 2- Wh
at do t
he Parameters p1 and p, in the hypotheses reprwent' 3. -
(ﬁsh-1% method would you use?
-sa.mp1e 'r (b) I—sample z (c) 2-sample T (d) 2-sample Z 4. -
fSSummog the POPUIation standard deviations are unknown but equal, calculate the
est statistic and ﬁnd the critical region. 5. What is your conclusion? Is zinc mass different for the 2 brands of batteries on
average? 6. How would you graphically check the assumption that the two populations are
normal? Problem 5. (4 + 2 + 3 + 6 + 4 = 19) We would like to know if listening to Rap and Classic music have different effect on learning. That is, if average number of objects
remembered while listening to Rap is different from that remembered while listening
to Classic music. To answer this question, each of 30 students listened to Rap music while attempting to memorize objects pictured on a page. They were asked to list all
objects they could remember and the number of objects remembered by each student was recorded. Then each student repeated the same process for Classic music. The
mean and standard deviation for number of objects remembered while listening to Rap and Classic music are given below. Mean and standard deviation for difference data are also given below.
I Mean SD. Rap 10.72 3.79
Classic 9.00 3.59
Difference = Classic - Rap -1.72 3.5 1. State the null and alternative hypotheses. (b) I‘Smple Z (c) 2-sample T (d) 2-sample Z e .
'o 95% Conﬁdence interval for the mean difference, you can assume
:1 Standard deviations are unknown but equal if necessary. 5. Use the calculated conﬁdence interval above to test hypotheses given in part 1.
Does music type affect learning ability? Problem 6. (3 +6+3 +3+ 6+6 = 27) Researchers are interested in the effect of student
coffee consumption on exam performance. A sample of 55 students are taken from a large
calculus class and each student’s daily coffee consumption (oz/day) and ﬁnal exam score
(%) are recorded. Summary statistics: )7=25,sx =12,?=80,3y =3,r=0.8 1. In view of the question the researchers want to answer, what is the independent
variable, and what is the response variable? 2. Find the least squares regression equation. 4. Is the model overestimating or underestimating for a person who drinks 30 oz / day
and scores 80%? 5. Answer the following questions by ﬁlling in the blanks based on the interpretations
of a and ,6. c When the coffee consumption increases by 1 02/ day, on average the exam score will ________________________ o For those who do not drink coffee, on average the exam score is 6. Find the 95% conﬁdence interval for the slope [5' of the regression line. Does the
95% C.I. support the claim that ﬂ > 0? Problem 7. (4 + 7 = 11) A random sample of 100 data points was collected to test if
the population mean u is lower than 24000 at a = 0.05 level. That is, Ha : p = 24000 vs. H1 : p < 24000 2. Suppose that the tr the Pr0bability ﬁ 0 hove, ﬁnd
ue Population mean is actually 23600. For the test a.
f comitting a Type II error. ...

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