1. True

or False. Justify for full credit score. (25

pts)

(a) If

there isn’t a linear correlation between two variables, then these two variables

usually are not associated in any manner.

STAT200 : Introduction to

Statistics Last Examination, Fall 2014 OL4 /

US2 Web page

2 of 6

(b) If

the variance from an information set is zero, then all of the observations on this information

set are an identical.

(c) P( A

and A)=1, the place Ais the

complement of A.

(d) In

a speculation testing, if the P-value is lower than the importance stage ?, we

reject the null speculation.

(e) The

quantity of milk in a jug of milk is 128 oz. The worth 128 is from a discrete

information set.

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Confer with the next frequency distribution for Questions

2, three, four, and 5. Present all work. Simply the reply, with out

supporting work, will obtain no credit score.

The frequency distribution beneath exhibits the distribution for

checkout time (in minutes) in UMUC MiniMart between three:00 and four:00 PM on a

Friday afternoon.

Checkout Time (in minutes)

Frequency

1.zero – 1.9

2

2.zero – 2.9

12

three.zero – three.9

2

four.zero – four.9

four

2.

What share of the checkout instances was lower than three

minutes?

(5 pts)

three.

In what class interval should the median

lie? Clarify your reply.

(5 pts)

four.

Calculate the imply of this frequency distribution.

(5 pts)

5. Calculate

the usual deviation of this frequency distribution. (Spherical the reply to 2

decimal

locations) (10

pts)

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Confer with the next information to reply questions 6, 7 and

eight. Present all work. Simply the reply, with out supporting work,

will obtain no credit score.

A random pattern of STAT200 weekly research instances in hours is as

follows:

2

15

15

18

40

6.

Discover the pattern customary deviation. (Around the

reply to 2 decimal locations)

(10 pts)

7.

Discover the coefficient of variation.

(5 pts)

eight. Are

any of those research instances thought of uncommon primarily based on the Vary

Rule of Thumb?

Present work and

clarify. (5

pts)

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Confer with the next data for Questions 9, 10 and

11. Present all work. Simply the reply, with out supporting

work, will obtain no credit score.

Contemplate deciding on one card at a time from a 52-card deck.

Let occasion A be the primary card is an ace, and occasion B be the second card is an

ace. (Word: There are four aces in a deck of playing cards)

STAT200

: Introduction to Statistics Last Examination, Fall 2014 OL4

/

US2 Web page

three of 6

9. If

the cardboard choice is with out substitute, what’s the chance that the

first card is an ace and

the second

card can also be an ace? (Specific the reply in easiest fraction

kind) (10

pts)

10. If

the cardboard choice is with substitute, what’s the chance that the primary

card is an ace and

the

second card can also be an ace? (Specific the reply in easiest

fraction kind)

(10 pts)

11.

Are A and B unbiased

when the choice is with substitute? Why or why not?

(5 pts)

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Confer with the next data for Questions 12 and

13. Present all work. Simply the reply, with out supporting

work, will obtain no credit score.

There are 1000 juniors in a school.

Among the many 1000 juniors, 200 college students are taking STAT200, and 100 college students are

taking PSYC300. There are 50 college students taking each programs.

12. What

is the chance that a randomly chosen junior is taking not less than one in every of

these two

programs? (10

pts)

13. What

is the chance that a randomly chosen junior is taking PSYC300, given

that

he/she is taking

STAT200? (10

pts)

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14. UMUC

Stat Membership should appoint a president, a vp, and a treasurer. There

are 10

certified candidates. What number of other ways can the

officers be appointed? (5

pts)

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15. Mimi

has seven books from the Statistics is Enjoyable sequence. She plans on bringing three

of the seven

books with

her in a street journey. What number of other ways can the three books be

chosen? (5 pts)

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Questions

16 and 17 contain the random variable x with chance

distribution given beneath.

Present all

work. Simply the reply, with out supporting work, will obtain no credit score.

x

-1

zero

1

2

P( x)

zero.1

zero.three

zero.four

zero.2

16.

Decide the anticipated worth of x.

(5 pts)

17.

Decide the usual deviation of x. (Spherical

the reply to 2 decimal locations)

(10 pts)

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Contemplate the next state of affairs for Questions 18, 19 and

20. Present all work. Simply the reply, with out supporting

work, will obtain no credit score.

Mimi simply began her tennis class three weeks in the past. On

common, she is ready to return 20% of her opponentâs serves. Assume her

opponent serves eight instances.

18. Let

X be the variety of returns that Mimi will get. As we all know, the distribution of X is

a binomial

chance distribution. What’s the variety of trials (n),

chance of successes (p) and

chance of failures (q),

respectively? (5

pts)

STAT200 : Introduction to

Statistics Last Examination, Fall 2014 OL4 / US2

Web page four of 6

19.

Discover the chance that that she returns not less than 1 of

the eight serves from her opponent.

(10 pts)

20.

What number of serves can she anticipate to return?

(5 pts)

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Confer with the next data for Questions 21, 22, and

23. Present all work. Simply the reply, with out supporting

work, will obtain no credit score.

The heights of dogwood timber are usually distributed with a

imply of 9 toes and a typical deviation of three toes.

21.

What’s the chance that a randomly chosen dogwood

tree is bigger than 12 toes?

(5 pts)

22.

Discover the 75th percentile of the dogwood

tree peak distribution.

(10 pts)

23. If

a random pattern of 36 dogwood timber is chosen, what’s the chance that

the imply peak

of this pattern is lower than 10

toes? (10

pts)

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24.A

random pattern of 100 mild bulbs has a imply lifetime of 3000 hours. Assume that

thepopulation customary deviation of the lifetime is 500 hours.

Assemble a 95% confidence interval estimate of the imply lifetime. Present

all work. Simply the reply, with out supporting work, will obtain no

credit score.(15 pts)

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25. Given

a pattern measurement of 100, with pattern imply 730 and pattern customary deviation 100,

we carry out the next speculation check on the a = zero.05

stage.

H0 : m=750

H1: mÂ¹750

(a) Decide

the check statistic. Present all work; writing the right check statistic,

with out supporting work, will obtain no credit score.

(b) Decide

the vital values. Present all work; writing the right vital worth, with out

supporting work, will obtain no credit score.

(c) What’s your conclusion of the check? Please

clarify. (20

pts)

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26. Contemplate

the speculation check given by

H0 : p=zero.5

H1: p<0.5 In a random sample of 225 subjects, the sample proportion is found to be pË = 0.51. (a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 5 of 6 (b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. (c) Is there sufficient evidence to justify the rejection of H0 at the a = 0.01 level? Explain. (20 pts) .gif">.gif”>.gif”>.gif”>

27. In

a research of reminiscence recall, 5 individuals got 10 minutes to memorize an inventory of

20 phrases. Every was requested to record as most of the phrases as she or he might

bear in mind each 1 hour and 24 hours later. The result’s proven within the following

desk.

Variety of Phrases Recalled

Topic

1 hour later

24 hours later

1

14

12

2

18

15

three

11

9

four

13

12

5

12

12

Is there proof to counsel that the imply variety of phrases

recalled after 1 hour exceeds the imply recall after 24 hours?

Assume we wish to use a zero.01 significance stage to check the declare.

(a) Establish

the null speculation and the choice speculation.

(b) Decide the

check statistic. Present all work; writing the right check statistic,

with out supporting work, will obtain no credit score.

(c) Decide

the vital worth. Present all work; writing the right vital worth, with out

supporting work, will obtain no credit score.

(d) Is there

enough proof to assist the declare that the imply variety of phrases recalled

after 1 hour exceeds the imply recall after 24 hours? Justify your conclusion.

(20 pts)

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Confer with

the next information for Questions 28 and 29.

x

zero

-1

three

5

y

three

-2

three

eight

28. Discover

an equation of the least squares regression line. Present all work;

writing the right

equation, with out supporting work, will obtain no credit score. (15

pts)

29. Primarily based

on the equation from # 28, what’s the predicted worth of y if x =

four? Present all work

and justify your reply. (5

pts)

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STAT200 : Introduction to Statistics

Last Examination, Fall 2014 OL4 / US2

Web page 6 of 6

30.

The UMUC MiniMart sells 4 several types of teddy

bears. The supervisor stories that

the 4 sorts are equally standard. Suppose that a pattern

of 100 purchases yields

noticed counts 30, 24, 22, and 24 for sorts 1, 2, three, and

four, respectively.

Kind

1

2

three

four

Quantity

30

24

22

24

Assume we wish to use a zero.10 significance stage to check

the declare that the 4 sorts are

equally standard.

(a)

Establish the null speculation and the choice

speculation.

(b)

Decide the check statistic. Present all work;

writing the right check statistic, with out

supporting work, will obtain no credit score.

(c)

Decide the vital worth. Present all work;

writing the right vital worth,

with out supporting work, will obtain no credit score.

(d)

Is there enough proof to assist the managerâs

declare that the 4 sorts are

equally standard? Justify your reply.

(20 pts)