AP STATISTICS Inference Take Home Test

8/12/2019 AP STATISTICS Inference Take Home Test

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AP STATISTICS NAME: ____________________________

INFERENCE(sample means and proportions)

MULTIPLE CHOICE: Choose the best answer from the answer choices.

1. You have sampled 25 students to find the mean SAT scores at orris !nolls "i#h School. A $5% confidence interval for themean SAT score is $&& to 11&&. 'hich of the followin# statements #ives a valid interpretation of this interval

(A) $5% of the 25 students scored between $&& and 11&&.

() $5% of the population of all students at orris !nolls "i#h School have a score between $&& and 11&&.(C) *f this procedure were repeated man+ times, $5% of the resultin# confidence intervals would contain the true mean of

orris !nolls "i#h School.

(-) *f this procedure were repeated man+ times, $5% of the resultin# confidence intervals would be between $&& and 11&&.

() *f 1&& samples were ta/en and a $5% confidence interval was computed, 5 of them would be in the interval $&& to 11&&.

2. A candidate for ma+or hires a statistician to determine the amount of support he has for the up comin# election. The

statistician tests the null h+pothesis that the population proportion e0uals 5&% a#ainst the alternative h+pothesis that the

population proportion is #reater than 5&%. The results of a simple random sample of $1 re#istered voters can be found in theprintout below.

Test of p &.5 vs p &.5

Success for candidate

3ariable 4 Sample 6 7act 6 value

8or candidate 59 $1 &.:;

*. The candidate can be 0uite confident that he has more than 5&% of the vote.

**. Thep?value of &.&&== tells us that we cannot re@ect the null h+pothesis and that the candidate has 5&% or less ofthe vote.

***. Thep?value of &.&&== indicates that it is not ver+ li/el+ to #et an observed value of &.:;< if the nullh+pothesis is true.

(A) * onl+

() ** onl+(C) *** onl+

(-) * and **

() * and ***

;. *n each of the followin#, thep?value and the si#nificance level are #iven for a test of h+pothesis. 'hich pair of valueswarrants a re@ection of the null h+pothesis

(A) p?value &.&;12, &.&1

() p?value &.&=11, &.&5(C) p?value &.&52$, &.&5(-) p?value &.&:


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(-) * and **

() ** and ***

5. 'hich of the followin# are the characteristics of a t?distribution curve

*. The #raph of a t?distribution e7tends infinitel+ to the left and to the ri#ht and approaches thex?a7is as+mptoticall+asxincreases in absolute value.

**. There are an infinite number of different t?curves, each determined b+ a parameter called the de#rees of freedom.***. The ma7imum point on the #raph of a t?distribution occurs at its mean which is alwa+s &.

(A) * onl+() ** onl+

(C) *** onl+

(-) * and *** onl+() *, **, and ***

:. *n conductin# a h+pothesis test, thep?value is the

(A) 6robabilit+ of obtainin# a result as e7treme or more e7treme than the one obtained than the one obtained if the null

h+pothesis is true.() Si#nificance level of the test

(C) 6robabilit+ of ma/in# a T+pe * error

(-) 6robabilit+ of ma/in# a T+pe ** error

() 6robabilit+ that the null h+pothesis is true

1=& ft.

() "o> D 1=& ft. "a> E 1=& ft.

(C) "o> 1=& ft. "a> 1=& ft.(-) "o> 1=& ft. "a> 1=& ft.

() "o> 1=& ft. "a> 1=& ft.

9. *n a sample surve+ of =5& residents of a #iven communit+, 19& of them indicated that the+ shop at the local mall at least onceper month. Construct a $5% confidence interval to estimate the true percenta#e of the residents who shop monthl+ at the loca

mall.

(A) (&.;55, &.=55)

() (&.;::, &.=;=)(C) (&.; 2& at a si#nificance level ofalpha. *f the same procedure is used to test "o> 2& a#ainst "a> >2& with the same data then thep?value will

(A) *ncrease

() -ecrease

(C) Femain the same

(-) e doubled

() e decreased b+ one


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1&. A radio tal/ show host with a lar#e listenin# audience is interested in the proportionpof adults in his listenin# area that thin/the Bnited States should not be at war in Af#hanistan. "e as/s the 0uestion to his listeners, G-o +ou thin/ the Bnited States

should be at war in Af#hanistanH "e as/s his listeners to phone in and vote G+esH if the+ a#ree that the Bnited States should

be at war in Af#hanistan and no if the+ disa#ree. If the 1&& people who phoned in 95% answered G+esH. 'hich of thefollowin# assumptions for inference about a proportion usin# a confidence interval are violated

(A) The data are a simple random sample from the population of interest.

() The population is at least 1& times as lar#e as the sample.

(C) The sample siJe nis so lar#e that both the count of successes npand the count of failures n(1?p) are 1& or more.(-) 'e are interested in inference about a proportion.

() There appear to be no violations.

11. 8ive tablets of headache medicine T too/ an avera#e of :5 seconds to dissolve with a standard deviation of 1.; seconds. 8ivetablets of headache medicine A too/ an avera#e of :9 seconds to dissolve with a standard deviation of 1.2 seconds. *f we

assume that the dissolvin# times are normall+ distributed and the population standard deviation is the same for both medicine

A and medicine T, compute a $5% confidence interval for the difference in dissolvin# time (in seconds) between brands A

and T. Calculate usin# ei#ht de#rees of freedom.

(A) ; K 1.=


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'hat is the number of de#rees of freedom associated with a t?test to determine if there is a difference between the number of

aces served usin# the two rac/ets

(A) :

() 1&

(C) 11

(-) 12() 2=

1=. 8ind the value of the appro7imate test statistic for the #iven h+pothesis test.

"o> 59.2 x 5:.95

"a> 59.2 s =.9&

&.&1 n 1:

(A) ?=.5&

() ?1.125

(C) ?&.291(-) 1.125

() =.5&


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FREE RESPONSE: Show all +our wor/. *ndicate clearl+ the methods +ou use because +ou will be #raded on the

correctness of +our methods as well on the accurac+ and the completeness of +our results and e7planations.


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AP STATISTICS Inference Take Home Test

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