Group Problems - Hypothesis TestingCIVL 3103

1. Suppose that an engineering firm is asked to check the safety of a dam. Whattype of error would it commit if it erroneously rejects the null hypothesis that thedam is safe? What type of error would it commit if it erroneously accepts the nullhypothesis that the dam is safe? What would the likely impact of these errors be?

-,2. An experiment was performed to compare abrasive wear of two different

laminated materials. Twelve pieces of material 1 were tested by exposing eachpiece to a-machine measuring wear. Ten pieces of material 2 were similarlytested. In each case, the depth of wear was observed. The samples of material 1gave an average wear of 85 units with a sample standard deviation of 4, while thesamples of material 2 gave an average of 81 and a sample standard deviation of 5.Can we conclude that the abrasive wear of material 1 exceeds that of material 2by more than 2 units? Use a p-value to determine your answer. Assume thepopulations to be approximately normal with equal variances.

3. Arsenic concentration in public drinking water supplies is a potential health risk.An article in the Arizona Republic (Sunday, May 27, 2001) reported drinkingwater arsenic concentrations in parts per billion (ppb) for 10 metropolitan Phoenixcommunities and 10 communities in rural Arizona. The data are shown in thetable below. Determine if there is any difference in mean arsenic concentrationsbetween metropolitan Phoenix communities and communities in rural Arizona atthe ex = 0.05 level of significance. Assume the populations to be approximatelynormal with unequal variances.

Metro Phoenix Rural ArizonaPhoenix, 3Chandler, 7Gilbert, 25Glendale, 10Paradise Valley, 6Peoria, 12Scottsdale, 25Tempe, 15Sun City, 7Mesa, 15

Rimrock,48Goodyear, 44New River, 40Apachie Junction, 38Nogales, 21Black Canyon City, 20Sedona, 12Payson, 1Casa Grande, 18Buckeye, 33

4. An article in the Journal of Strain Analysis (1983, Vol. 18, No.2) comparesseveral methods for predicting the shear strength for steel plate girders. Data fortwo of these methods, the Karlsruhe and Lehigh procedures when applied to ninespecific girders, are shown in the table below. Determine whether the KarlsruheMethod produces higher strength predictions on average than does the Lehighmethod, at the a = 0.0 I level of significance.

Girder Karlsruhe Method Lehigh Method1 1.186 1.0612 1.151 0.9923 1.322 1.063

4 1.339 1.062

5 1.200 1.065

6 1.402 1.178

7 1.365 1.037

8 1.537 1.086

9 1.559 1.052

0rv0£ 'Prt6lLrm

~o1hUis Tehhrij

1. Ho:~c~~

I+a ~ ~I;t VJ 1L61- stek t:

tk~ .Nj-Q.cf Hv ~~. T ~

~4 rJ..edpt Ifo 3? '0fX- ]I ~.7Jt~ "-+ 7T ~ ~~fr ~ ~;pi;

~~~~~~jt_Jiux~~ ~p~ 1I J-NLfVtJ .~ I ~ WJj re ~d.bf~- Ji w-e nVJu· tLJ0p.- if ~~ ) ~~~ W/UFt~~~~.

.-J :: O.'d.-r

SJ) z: 0 1133(,

+h : ,)JJ.o::::: 0

J..-ht ~?D~o

T~, ·f.;£lJIMOJ -= d -60. Oldl-O_c:~~~ ----".> <= _ ""J. q "l

~ IP\l OI13S0/fOIl

+pMwJ'7 i 01 ) ()-I

-t i 0 \ ) '2> -=- d I 3CJ ~

~(qt /'" J. ,~q lo (I2-U6 ~

~ut- .i-J-n. 'L~ ~.~ ~ J~oJ-o{~,6( t,&-;!;~~

-p~~~%4n,~fV1JJ1I\ATlo ~ .JY00-l- +t~ ~ttWQ 7 ili-wl ,·hud- <-J1\L j(~~m _ ~ '()Jlol~ ~ ~~~ I 1N~. (J~---

37

25106

1225157

15

Column 1

MeanStandard ErrorMedianModeStandard DeviationSample VarianceKurtosisSkewnessRangeMinimumMaximumSumCountConfidence Level(95.0%)

12.52.414079074

117

7.63398832758.27777778

-0.4382033720.767040306

223

25125

105.461026259

0.119 Column 10.1590.259 Mean0.277 Standard Error0.138 Median0.224 Mode0.328 Standard Deviation0.451 Sample Variance0.507 Kurtosis

SkewnessRangeMinimumMaximumSumCount

0.2735555560.045186684

0.259#N/A

0.1355600520.018376528

-0.5606044930.687695234

0.3880.1190.5072.462

9

484440382120121

1833

Column 1

MeanStandard ErrorMedianModeStandard DeviationSample VarianceKurtosisSkewnessRangeMinimumMaximumSumCount

27.54.853978895

27#N/A

15.34962902235.6111111

-0.988830641-0.288143481

471

48275

10

(;

TDiST (I, 04 I 'ZO ) I) := [J. ,oS S

(' \.j)/ LL~ ,~~, ~~ b-01}/tct Q ) r c.a:«: ~6 ckkA~G ~-P l,LttLcLL (,9'/ 0, fa, ) \ !

jlu;; 0 007:: 0h~_j4~o.-- -jD~L,uf /Ui

-/-UL>c,, cr 66 c /'

dlu~t h;(rdi~~- c~ I>-L ~dxd {1.-Cr: °6Yit1Z. a£le'l/l-Za/-cJ"'C. aLLe~~L cl =·0, I s-: i

B" rr~u-hw_ ~U&JL/

11(h-;:;::' {O (\ <c :::c ID

-~~t:::: IS< cS v: \tL,-;;L1 t ~

c -::::7dJ.? 4 s: /1 S (S3 SCytl\. It:--

c-~; '0;: 0(0)

-t--, (3v1;~ Stt-v''l/..f'~ ) 6"i, ,I 6L ( LL~dL-.0~"G)

,f/o :,)AJ(VI, -- !,,uL ::::.0

'-I· -bIIDW-zL \ /{.,-utvl - / - s. -