L.

C.... -

.

1.

2.

4. 3.

JA

5. 6.

J.2.0537

and

(a) a (b) (ç) interval.

(d) (c) (a)16 (b)271 (a) value (c) (d) (0.42 (b) (c) SAT-M test (e) (a)

report (a)90% interval (d) (b)95% Which You (e)over99.9%

(c) (a)

sample

You

You A

In

Suppose A

38 1.960 1.645 1.7507

Say Say Reject Reject 1476

A 99.5% significance the A A

0.29

certain

0.21 0.20 0.40

this

collect

a

of

99% 95% 95% 99%

want

want

test

that

of

test

that that sample

is

the

year

Assume

size

the

Ho Ho

of

that

says, confidence confidence confidence confidence this

data

population to

to

test

the the

following

follows

of Ho:

at at

compute

estimate

size

year,

the

test

probability the the

and

statistic.

“On

that

p

population =

is

gives

5%

1%

test

a

a the

a

50.

100

follows

interval interval interval interval

is normal

confidence

the

a =

significance significance

t —

true?

the

basis

96%

AP

a The

against

100. The .

that that

mean

p-value

hypothesis

STATISTICS

a

distribution

for for for for of

p-value confidence

of

value —-

normal Ho Ho

If

the

a

SAT - p p p p

you

Ha:

interval

simple

is is

will will will of will

level level

of

scores

false true

score

p

0.04. want of

distribution

z

include include include include ---

Ho:

*

the

interval

with

is for -

random

to

100, is — - ..

of for the

0.04

p

From test 0.04

be

CHAPTER

p =

all ‘-

mean

the

the the the a

a

is

margin

used

1

population

is

sample high

for

512.00

sample

and this

with

value value value value

thus

p

a

in ‘U.”-

school

we

and Ha:

population

of

this

mean

10

equal

of 0. 0.

1. 1.

±

error

of

can

p

standard

REVIEW

size

25.76.”

calculation

of

100

* seniors

p -

to

students -

to

1.

80 and —-

high

You

mean. be

produces _--

The

standard

deviation

who

approximately .0 school

obtain —

is

. with

confidence -

2.2_ Assume .

took

z= seniors a

a

deviation

a

the 90%

p-value =

0.8

that

SAT -

100. -

level

10,

confidence

that

for —

a

of

Math

a

you

the

You =

for

took =

0.022.

:—.. -U,

10 U

2.5.

will

this

read

I

the

need

a U ______

- 7. The government claimsthat students earn an average of $4500 during their summer break. A random sample of students gave a sample average of $3975 and a 95% confidenceintervalwas found to be $3525 < p < $4425. This intervalis interpreted to mean that: (a) If the study were to be repeated many times, there is a 95% probabilitythat the true average summer earnings is not $4500 as the government claims. (b) Becauseour specificconfidenceintervaldoes not containthe value $4500, there is a 95% probabilitythat the true average summer earnings is not $4500. (c) If we were to repeat our survey many times, then about 95% of allthe confidenceintervalswill containthe value $4500. If we repeat our survey many times, then about 95% of our confidenceintervalswillcontainthe true value of the average summer earnings of students.

8. To determine the reliabilityof experts used in interpretingthe results of polygraph examinationsin criminalinvestigations,280 cases were studied The results were

I TRUESTATUS I [INNOCENTLGuILrJ ‘ EXAMINER’S“INNOCENT”I131 T15L_- ‘c / DECISION “GUILTY” 1125 1 If the hypotheses were Ho: suspect is innocentvs. Ha: suspect is guilty,then we couldestimate the probabilityof makinga Type II error as (a) 15/280 (b) 9/280 L(ED15/140 9/140 (e) 15/146

9. A student is helping another student learn about confidence intervals. He says to her, “I am 95% confident that all of the test scores lie between 75 and 83”. Comment on his sentence.

10. When asked to explain the meaning of “the P-value was P = 0.03”, a student says, “This means there is only a 3% chance that the null hypothesis is true.” Is this a correct explanation? Explain.

11. Randomly selected students participated in an to test their ability to determine when 1 mm (60 seconds) has passed. Forty students yielded a mean of 58,3 sec. (a) Assuming that a = 9.5 sec, construct a 95% and state in a sentence your findings. (b) Is it likelythat students can determine when exactly 1 minute has passed? (C) Find the sample size to have a margin of error no bigger than 2.

12. In the past, the mean score of the seniors at Valley High on the ACTcollege entrance exam has been 20. This year a special course is offered, and all 53 seniors planning to take the ACTtest enroll in the course. The mean of their AT scores is 22.1. The principal believes that the new course has improved the students’ ACTscores. Assume that ACTscores vary normally with a = 6. Test the principal’sclaim at the 1% level by stating the null and alternative, drawing a picture, stating the test statistics and p-value, whether you reject or retain, and finally a complete sentence stating your conclusion. Based on your answer, what error could you have made?

13. The probability that a senior dares to cut Miss Biro’sclass after Disney is 12%. This year Miss Biro has 135 students. What is the probability that more than 17% willcut her class?

MULTIPLECHOICEANSWERS: D, B, B, D, C, C, D, C — 6 a

t flA yfl 4-—- $0 25 1’. ,l i 1 -o p L fl p C 1 ) IF I P — ‘1 r - cPo CD r p , L p G P ) o £ 3 0 1 fr, p p ‘1 Ic’ p ) p ‘I P 31 - t$1 ) p 5j? pp 3 S ii I ) / C p ° ‘ t-} ch’ V 2 Sr4 P c r 0 r U) < I F V -o ; C 4 II I It C C 7J H 1 .,( P ;P I’ IL) c f I C “p P r C p p C so I ) C yd-o o ail 2 t 2 C iPvJfs — (-%LP I 0 ç-o 1’ (S 35p 3 4 C’r H1 0 pG I p ‘p C t ‘ 2 P ‘9 UI C 4 r A (1 2 F’ r at ?- if IL) p p Ft 4, 3 1> 14 U 2 -* r I, 0 ) C ‘3 ) V1 ) -t a1 it 4 4 ci 2 P *1 C) of ?*10 —3, V 0 p p 2 I 6 C r r LI / ‘p

a (1 ii 3 1 m 7 ) p ) 1’ m ? r & 1j9 lb C r ‘ I ‘1’ ?‘ (p

if I j ,r 8 I, 1 ) 4? & íA 3 5 ° o’ &

0 ,; r C qh1 6 $5 3 4’ U ‘

C’ £ (% •r i 0 P r 1 f*J L‘I — S SW £1 ; ) 2 0 I 1’ 8 p ,i p •1 -V ) £ L 44 — a r 1” \

—

\

C

T