NAME: XXXXXXXXXXXX Kehe~ Mu rre II SECTIONAssume distrihution of amounts spent on food by fans is normally distributed. a. ( 4pts) What are the appropriate null and alternative hypothesis

WORKSHEET 8: Chapter lOa - Hypothesis Tests (Mean and Proportion)

NAME: Kehe~ Mu rre II

SECTION: ooS ---~--------~---~

Worksheets are to be completed as individual work.

On my honor, I have neither given nor received inappropriate or unauthorized information during the completion of this worksheet.,

Student's Signature: _ __.K.........,.,UAt..u-=...;-=+-----~-----· ---.....· ..;...• ----------------------\

1 . The concession manmzers for the Arkansas Travelers (a minor leai:rne baseball team located in Little Rock) are interested in estimating the average amount spent on food by fans attending the team's Frida~­night home games. Suppose a random sample of 26 rece1p::::; for iood o:ric~ -,,y:;::; L:i~'~Cil .ir~n:::. l~:;~ :. ~ ~=--· ;_

~~·~~3Y~ .. N~~ht~~F."p~!!d!hn·e~ _·d~ on RH). Assume distrihution of amounts spent on food by fans is normally distributed.

a. ( 4pts) What are the appropriate null and alternative hypothesis to determine it there is sutlicient evidence to suggest the mean amount spent by all Friday night football fans is different from

"'rnn, r1 o ·• fa1 = \ ~ / wht..ft. ~ i$ t~e. ftifUlcthu"l rnea~ a\'\'l\)\.H11 ( $) HA: ._,Lf f, 1 V ~r~ot b~ <1\\ f:tidtt~ °'jh1 foot~H tons.

b. ( 4 pts) What are the conditions needed to perform the appropriate test? Are these conditions met

and why? \ , raVld~ ~uwip le N.~ ~ 1ttv'jet fopu lQt\Cffl ~ ~es , st<\ted \fl p~~te"V\ ~

2. i i~ rnndo.¥''~ ~\Sthbuietl =?

l\tc;, '\ht pcfUldtltl)1 \S VO'H•(tlAt di~tn~e~ .

c. ( 5pts) What is the test statistic for your hypothesis test? Show notation, formula, and

calculations. j_- )-ii : x.-.:_• o l~.<;lf- l'l 'lob~ :: JV\ ~ - - , 9 2 ~

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d. ( 4 pts) What is the rejection region for your hypothesis test at a 0. 01 significance level? Draw an appropriate picture Jf~ 1 . .'5

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e. ( 1 Opts) Based on your answers above does there seem to be convincing statistical evidence that the mean amount spent by all Friday night football fans is different from $19? Explain and Justify your conclusion using your answers above.

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f. ( 12pts) Use Minitab to perform the appropriate hypothesis test. Embed or Attach Minitab output AND comment on why the output results in the same decision that you gave in part e.

Not of\\j d.\d_ Mlt'\\~ J•\ft. ~ the. Stl~ ~·stf.lkistic. , '~ ·rr ~\c;o jtlAIC-- me. q P ~allU of-. ?bo. Sec.a\ls~ _ 1\t\, S P Volt.Lt tS j t'ec,t4er t \tJQh t"e a \ph4 1)f . o \ we WO\A t<;;J fcii( -b ':j e.c:t "«ll h~rothec;,~ <1S well. (~ aitocl;ed plqe fut I Mltutalo fllSl' s)

Bonus: ( 5 pts) You used this same data to construct a 99% confidence' interval on your Chapter 9 worksheet. Can you briefly explain the relationship between that confidence interval and this two sided hypothesis test?

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2. The National Center for Drug Abuse is conducting a study to determine if heroin usage amount teenagers has changed. Historically, about 1.3 percent of teenagers between the ages of 15 and 19 have used heroin one ore more times. In a recent survey of 1824 randomly selected teenagers, 3 7 indicated they had used heroin one or more times. Is there overwhelming evidence of a change in heroin usages among teenagers? Test at the 0.05 level. " ?1

a. (4pts) What are the appropriate null and alternative h;pothe~i~'-o'fthe hypothesis test? \-\o .. " :. 0\ '3

· / whert.. f : rfU\O'.ilon ~~(llOn \\f\ ~ p :J: · 0 \ ~ of f"eel"\~.et'S Who htJ,c_ IASt.d ~~in

«ef\e. or rr..~ i\ ~·~.

b. ( 4pts) What are the conditions needed to perform the appropriate test? Are these conditions me

and why? 1. random ""mre. .fi.vm f\'.)F'-INl - l\ e-s, c;;;-«~cl \n ~

2... p mu.s1 i?e VlOvt'h~ cU<:-tiib"tkJ r•r~s ~l.-'?

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c. ( 6pts) What is the test statistic for your hypothesis test? Show notation, formula, and calculations.

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d. (6pts) What is the p-value for your hypothesis test? Show work.

2r (-e, z .--=r., 7-) ~ z.(.oa 3) -=- . ooG

e. (1 Opts) Based on your answers above does there seem to be convincing statistical evidence of a change in heroin usages among teenagers? Justify your conclusion using your answers above.

ot..=. o5 ... L..~ ~I~;~ A-1 ~ co·r~ ~i~ t1i1n-cah<.t \~, M'i _ ~ -. vu\VL 'ls less ~o> oe1 T~ . .':r' ..... t-~ OJ\\ ~~SIS, T\ie, d.atc.4 (»'OVI~ SU tie.tlt ~~(ti -\-hut ~ fp~lUt°'\

r·-orol\1 C2f teens who na...-e. \lSt.d ~roin \5 Ji~ 1hA.n f 0 l ~ I

f. (12pts) Use Minitab to perform the appropriate hypothesis test. Embed or Attach Minitab output AND comment on why the output results in the same decision that you gave in part e.

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3. A consumer group believes that a new sports coupe gets significantly fewer miles to the gallon than advertised on the sales sticker. To confirm this belief, they randomly select several of the new coupes and measure the miles per gallon.

a. (7pts) Develop the appropriate null and alternative hypothesis.

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w~ J.1 i~ -tlt&L f"r4\cJ1~ fl1(:,u, V'l'leJ of -the new "-r0ft6 UNpe- .

b. ( 6pts) State what the consequences of a Type I error would be for this situation

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c. ( 6pts) State what the consequences of a Type II error would be for this situation

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1f. One-Sample T: Expenditures

Test of µ = 19 vs ~ 19

Variable N Mean StDev SE Mean Expenditures 26 17.53 8.02 1.57

2f. Test and Cl for One Proportion

Test of p = 0.013 vs p * 0.013

99% CI (13.15, 21.92)

T p

-0.93 0.360

Sample X N Sample p 95% CI Z-Value P-Value 1 37 1824 0.020285 (0.013816, 0.026755) 2.75 0.006

Using the normal approximation.

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