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Unformatted text preview: STA 6126 — Exam 2 Last Name: First Name: UFID: Part I  Multiple Choice CLEARLY CIRCLE YOUR ANSWER.
Each question is worth 8 points for a total of 56. 1. A conﬁdence interval with a = 0.10 (that is a 90% CI) for the population parameter
p is (1333,1570). This means that the probability that u is between 13.33 and 15.70 is 0.90.
The probabiln‘tj that our Methodologj captures flu:
oFalse 'hrve mecm is (9.0m 2. A 95% Cl includes all the values of the population parameter estimate for which we
would reject the null hypothesis of a two sided test. x True A CI mclvcles plan/9MB Values (CV) in cm inkrvuk . . False R54 HO; :A0 and Llo K M (CU) +lxev1 l'l‘ l5
plwsible qncl wt —\o r‘vzthé Ho. 3. I want to know the mean number of customers that enter a store per hour. Using data
collected over the last month, a 90% conﬁdence interval for the mean number is (17.11,
25.12). A 95% conﬁdence interval of (16.38, 25.48) is also created. What is the correct
conclusion for the p—value associated with the hypothesis test of H0 : ,u = 25?
O
O The p—value will be greater than 0.10. N011 +lxm‘, 2.5 is in Th: (‘04 CI
K The pvalue will be between 0.05 and 0.10. {0 Vie +0 {96H H0 at Mfg
= — > o .
X The pvalue will be less than 0.05. em > V “we ‘ 0 )Q There is not enough information to make any of the above conclusions. 4. A researcher wants to test whether attending a marketing seminar for a product will
change customers perception of the product/service. The researcher has the 11 cus—
tomers rate the product before and after the seminar. Using what method will he
perform a hypothesis test? K Test for the difference between population proportions.
K Small—sample test for the difference between population means. X ; Large—sample test for the difference between population means.
@ "Test for paired data with t—score. lL is AQVQWCAQMf SlﬁCQ we (1 Uglvg 5. A sample of 100 components is drawn, and a 95% conﬁdence interval for the proportion
defective speciﬁes this proportion to within i 0.06. To get a more precise estimate of
the number of defective components, the sample size will be increased to 400, and the
conﬁdence interval will be recomputed. What will be the approximate total width of
the new conﬁdence interval? A \«A I‘ A A,
x 0.031 We have H6 1%; :0,06 9 f(\’)~0.0‘55Ly ‘ 0.00151! ~
00.060 5° Lch «7:50 A 0.030... x'0015 50 40M Mada/x is 2x0030 2006? 6. In a random sample of 120 individuals, the average time spent in the restroom per
month was 135 hours and the standard deviation was 12 hours. A researcher claims that
the mean time is between 132.452 and 137.548 hours. With what level of conﬁdence can this statement be made? X 95% Margin 0Q umr := ‘ﬁwzr 254g
99‘7 .. \7.
i 0 v) 2“92 ""‘" : 2.54% '/‘> 2,42: 233 o 98% \20 o 0‘
, ‘ I .
X 90% Loalduj at lablt 235 SW5 4% 7.33
g) :00‘ S) i=0'0'2' 57 7. A sample of 10 measurements is taken and assumed to be normal. The following are
summary statistics for this data set. Variable N Mean Median StDev SE Mean
X 10 13.040 13.100 1.009 0.319 Perform the hypothesis test H0 : a g 12 versus Ha : a > 12. Choose the best answer. X' p—value > 0.10 \3.OL\.~\2
X 0.05 < p—value < 0.1 : : 3 .2 6
X 0.01 < p—value < 0.05 o ' 3‘ q
® p—value < 0.01 ‘ ‘7'vi
4: 0.00056 x: The pValue cannot be determined. (1 Part II  Questions 1. (16 points) In a clinical trial to compare the effectiveness of two pain relievers, a sample
of 107 patients was given drug A, and an independent sample of 138 patients was given drug
B. Of the patients on drug A, 77 reported substantial relief, While of the patients on drug B,
126 reported substantial relief. Can you conclude that drug B is more effective than drug A
at the a = 0.05 signiﬁcance level? (Write all the steps of the process) i) Obtain your conclusion by a two—sided 95% CI. " V? A n 0 A " 0
A = / 2 O. 720 _ i Lqe “("930 (661's)
Y l0?L 9A Qﬁ in)? t are (I Q“, Pﬁhrg A
: ‘26 a
Y6 ,r—‘gb’ ‘oF’H3 :> (wuzqoe , 49.03152) / i o
Shae We Wth ts Sindlj neﬁwbwe => VA4 Va. ii) Obtain your conclusion by the appropriate (sided) hypothesis test. To 1&er i2 {5 is mum echﬁve than A => ﬁt?“ HO: VA’VfbaO V9 HQ: YA‘?¢540 — .23. \26
Ts: PA (5 \A‘QYe 6:")? ‘94 ragga
€<\~€’>(.‘;Jt‘g) “’H‘”
= 082‘36
: «5.“\8
400$ 2. (18 points) Tennis elbow is thought to be aggravated by the impact experienced when
hitting the ball. A sports physiologist reported the force (N) on the hand just after impact on
a one—handed backhand drive for six advanced players and eight intermediate players in the
following table. The data did not contain any outliers and appeared to be symmetric. Let
MX denote the (unknown) mean force for the advanced players and ﬂy for the intermediate players. Type of Sample Sample Sample
Player Size Mean Std. Dev.
Advanced (X) 6 40.3 11.3
Intermediate (Y) 8 21.4 8.3 i) Calculate a 95% conﬁdence interval for ,LLX, the mean force of impact for the advanced players.
’+ + g + 25:3 “‘2
Ir "Va015,5 m ~> 403’  (a; :> (23»; , 5216) ii) Calculate a 95% conﬁdence interval for ,uX — ﬂy, the difference in the average force
between the two groups. iii) Perform a a = 0.10 level hypothesis test, assuming equal variances, for the hypotheses
HOIHX*,UYSS, H13MX—#Y>8~ You should give bounds on the pvalue and clearly state the conclusion. (Use the back
of the page if you run out of room.) Ts :(i*558 _ (40.3’2l.H)—g
. \ I r 5 \ Wham 5‘,ka .— (“VOSKIIrCMWVI _ iStl\31+ 4. 3,31
:7 T, S : 2.0“1 (lg"111* €(aazs,o.os)
t”. ‘ .
o 1.... “We ‘40 . 3. (10 points) A sample of the same 10 diesel trucks were run both hot and cold to
estimate the difference in fuel economy. The results, in mpg, are presented below. 4.56 4.46 6.49 5.37 6.25 5.90 4.12 3.85 4.15 4.69
Cold 4.26 4.08 5.83 4.96 5.87 5.32 3.92 3.69 3.74 4.19 Find a 95% conﬁdence interval for the difference in mean fuel mileage between hot and cold
engines. What is your conclusion at the a = 0.05 signiﬁcance level? 6: 0.3% 39: 0455s ’/'> (0,2365 , (9.50ch) _‘l__€____§_
(Mamie VmﬂACOM ...
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 Spring '08
 YESILCAY
 Statistics, Null hypothesis, researcher

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