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[answered] 1) The expression ( P z /2 a) b) c) d) x + z /2 =1 n n ) me


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1) The expression ( P ??z? /2 a)

 

b)

 

c)

 

d) ?

 

?

 

? ?x ? ?+ z ? /2

 

=1??

 

?n

 

?n ) means:

 

a) In a random sample of size n, the probability that

 

is within ?

 

b) c) d) z?/ 2 ?

 

?n of ? is 1?? ?x . 1?? fraction of the means from samples of size n

 

deviate from the population mean by no more than ? 4) 5) The fraction of sample means from samples of size n = 49

 

that exceed $1,000 is,

 

a) 0.2207

 

b) 0.2451

 

c) 0.2810

 

d) 0.3050

 

The margin of error for interval which includes 95% of the

 

means from samples of size n = 49 is,

 

a) 70.56

 

b) 72.28

 

c) 74.84

 

d) 78.44 Next TWO questions are related to the results of the 2016

 

presidential election in Indiana.

 

In the 2016 presidential election Hillary Clinton received 38% of

 

the votes in Indiana.

 

6) In a random sample of n = 625 Indiana voters, what is the

 

probability that more than 40% voted for Clinton.

 

a) 0.1515

 

b) 0.1351

 

c) 0.1035

 

d) 0.0887

 

7) 840

 

1010

 

750

 

960

 

680 standard errors.

 

Once you take a specific sample and calculate the value

 

of ?x , you are 1?? ? percent certain that the

 

value you calculated is ?.

 

Both a and b are correct. For the same sample size n = 49, standard error of the

 

sample mean is,

 

a) 38.50

 

b) 37.25

 

c) 36.00

 

d) 34.75 The middle interval which includes 95% of proportions from

 

samples of size 625 voters is, You want to build an interval estimate of the average

 

monthly rent of two-bedroom apartments in Marion County.

 

You obtain a pilot sample of n = 5 apartments. The sample

 

yields the following data

 

x z?/ 2 Next FOUR questions are related to the following population

 

summary measures of weekly wage of workers in Indiana.

 

According to the Bureau of Labor Statistics, the average weekly

 

wage in Indiana is ? = $975. The standard deviation of weekly

 

wage is ? = 252.

 

2) For repeated random samples of n = 49 workers, the

 

expected value of the sample mean is:

 

a) 960

 

b) 975

 

c) 139.3

 

d) 19.9

 

3) 8) (0.348, 0.412)

 

(0.342, 0.418)

 

(0.336, 0.424)

 

(0.331, 0.429) Using this sample, the margin of error for a 95% confidence

 

interval is,

 

a) $192

 

b) $185

 

c) $178

 

d) $172

 

9) To build a 95% confidence interval for the mean monthly

 

rent with a margin of error of ?40, find the minimum sample

 

size, using $180 as the planning value.

 

a) 78

 

b) 85

 

c) 92

 

d) 98 10) You obtain a random sample of n = 90 two-bedroom

 

apartments. The sample mean is $860 with a standard

 

deviation of $182. The 95% confidence interval is then,

 

a) (814, 906)

 

b) (822, 898)

 

c) (832, 988)

 

d) (839, 981)

 

11) To build an interval estimate for the average commuting time

 

from his residence in Fishers to his work in downtown

 

Indianapolis, Tom kept track of his traveling time for a

 

random sample of 121 days. The interval he built had lower

 

and upper ends of, respectively, 44.36 and 47.64 minutes.

 

The sample standard deviation was 11 minutes. What is the

 

confidence level for Tom?s interval estimate?

 

a) 99%

 

b) 98%

 

c) 95%

 

d) 90%

 

12) Currently 360 students are taking E270. Suppose each

 

student is assigned to take a random sample of 100 workers

 

in Indiana and each build a 95% confidence interval for the

 

average weekly wage. How many of these 360 intervals

 

should we expect to capture the actual population mean

 

weekly wage?

 

a) 95

 

b) 100

 

c) 342

 

d) 350 13) Suppose a week before November 8, 2016 (election day) you

 

took a random sample of 510 likely Hoosier voters, 56

 

percent of whom indicated they would vote for Trump. You

 

wanted to build an interval estimate of the fraction of voters

 

such that 19 out of 20 such intervals included the proportion

 

of all likely voters in Indiana who favored Trump. The

 

margin of error for this interval was,

 

a) 0.043

 

b) 0.039

 

c) 0.036

 

d) 0.032

 

14) Referring to the previous question, you were asked to build a

 

similar interval but now with a margin of error of ?0.03 (3

 

percentage points). What was the minimum number of

 

voters that you had to include in your random sample? You

 

chose 0.55 as the planning value to determine the sample

 

size.

 

a) 1057

 

b) 1042

 

c) 1020

 

d) 1005

 

15) You are reading a report that contains a hypothesis test you

 

are interested in. The writer of the report writes that the pvalue for the test you are interested in is 0.1204, but does not

 

tell you the value of the test statistic. Using ? as the level of

 

significance, from this information you ______

 

a) cannot decide based on this limited information. You

 

need to know the value of the test statistic.

 

b) decide to reject the null hypothesis at ? = 0.10, and

 

reject at ? = 0.05

 

c) decide to reject the null hypothesis at ? = 0.10, but not

 

reject at ? = 0.05.

 

d) decide not to reject the null hypothesis at ? = 0.10, and

 

not to reject at ? = 0.05

 

16) According to the Bureau of Labor Statistics, the average age

 

at marriage for persons with a bachelor?s degree or higher in

 

the United States is 26.4. To test the hypothesis that the

 

average age at marriage in Indiana for person?s with similar

 

status is less than the national average, you select a random

 

sample of 105 such persons. The sample mean age is xx =

 

25.6 with a standard deviation of s = 3.9 years. The null and

 

alternative hypotheses for this test are,

 

a) H?: ? ? 26.4

 

H?: ? < 26.4

 

b) H?: ? > 26.4

 

H?: ? ? 26.4

 

c) H?: ? < 26.4

 

H?: ? ? 26.4

 

d) H?: ? ? 26.4

 

H?: ? > 26.4

 

17) The p-value for the hypothesis test in the previous question

 

is.

 

a) 0.056

 

b) 0.027

 

c) 0.018

 

d) 0.002

 

18) Given the p-value above, at a 5% level of significance,

 

a) do not reject the null hypothesis. Do not conclude the

 

mean age at marriage in Indiana is less than the

 

national average.

 

b) do not reject the null hypothesis. Conclude the mean

 

age at marriage in Indiana is less than the national

 

average. c)

 

d) reject the null hypothesis. Do not conclude the mean

 

age at marriage in Indiana is less than the national

 

average.

 

reject the null hypothesis. Conclude the mean age at

 

marriage in Indiana is less than the national average. 19) To test, at a 5 percent level of significance, if the average fill

 

of half-gallon milk containers is 32 ounces, a random sample

 

of 5 containers yielded the following data.

 

x

 

31.9

 

32.8

 

34.0

 

32.6

 

33.8

 

(Note: ?x? = 5454.65)

 

a)

 

b)

 

c)

 

d) TS = 2.62; CV = 1.960. Conclude the mean is different

 

from 32 ounces.

 

TS = 2.62; CV = 2.776. Do not conclude the mean is

 

different from 32 ounces.

 

TS = 2.98; CV = 2.776. Conclude the mean is different

 

from 32 ounces.

 

TS = 2.98; CV = 1.960. Conclude the mean is greater

 

than 32 ounces. 20) Advocates of the mass-transit system in a major

 

metropolitan district claim that more than 55% of the voters

 

would favor a tax hike to fund the expansion of mass-transit

 

system if the tax hike proposal was put to a public

 

referendum. To test this claim, at a 5% level of significance,

 

you select a random sample of 930 voters in the district and

 

find that 58.1% in the sample favor the tax hike. The null

 

and alternative hypotheses for this test are:

 

a) H?: ? > 0.55 H?: ? ? 0.55

 

b) H?: ? ? 0.55 H?: ? < 0.55

 

c) H?: ? < 0.55 H?: ? ? 0.55

 

d) H?: ? ? 0.55 H?: ? > 0.55

 

21) The probability value for this test of hypothesis is,

 

a) 0.017

 

b) 0.029

 

c) 0.038

 

d) 0.055

 

22) Based on the p-value in the previous question,

 

a) Reject the null hypothesis. Conclude the proportion

 

who favor the tax hike is greater than 0.55.

 

b) Do not reject the null hypothesis. Conclude the

 

proportion who favor the tax hike is greater than 0.55.

 

c) Reject the null hypothesis. Do not conclude the

 

proportion who favor the tax hike is greater than 0.55.

 

d) Do not reject the null hypothesis. Do not conclude the

 

proportion who favor the tax hike is greater than 0.55.

 

23) To test the hypothesis that the percentage of individuals with

 

four years of college education who smoke has decreased

 

from 21% a decade ago, a random sample of 1000 such

 

individuals revealed that 188 smoked. Use ? = 0.05.

 

Compute the p-value. a) b) c) d) p-value = 0.044. Do not reject H?. The sample

 

proportion is not significantly less than 21%. Do not

 

conclude that the proportion of college educated

 

individuals who smoke has decreased compared to a

 

decade ago.

 

p-value = 0.064. Reject H?. The sample proportion is

 

significantly less than 21%. Conclude that the

 

proportion of college educated individuals who smoke

 

has decreased compared to a decade ago.

 

p-value = 0.044. Reject H?. The sample proportion is

 

significantly less than 21%. Conclude that the

 

proportion of college educated individuals who smoke

 

has decreased compared to a decade ago.

 

p-value = 0.064. Do not reject H?. The sample

 

proportion is not significantly less than 21%. Do not

 

conclude that the proportion of college educated

 

individuals who smoke has decreased compared to a

 

decade ago. 24) The following data for a sample of 10 individuals shows the

 

hourly earnings and years of schooling.

 

Hourly

 

Earnings

 

$17.24

 

15.00

 

14.91

 

4.50

 

18.00

 

8.29

 

21.23

 

14.69

 

10.21

 

42.06 Years of

 

Schooling

 

15

 

16

 

14

 

6

 

15

 

12

 

16

 

18

 

12

 

22 The following calculation are done for you:

 

?y = 166.13

 

?x = 146

 

?xy = 2755.76

 

?x? = 2290

 

?(x ? xx )(y ? yx ) = 330.262

 

?(x ? xx )? = 158.4

 

The prediction error for a person with 18 years of schooling is,

 

a) -$9.01

 

b) $8.16

 

c) $7.09

 

d) -$6.28 e)

 

f)

 

g) h)

 

i) j) Next SIX questions are based on the following regression model In a regression model relating the price of homes (in $1,000) as the dependent variable to their size in square feet, a

 

sample of 20 homes provided the following regression output. Some of the calculations are left blank for you to

 

compute. k)

 

q) SUMMARY OUTPUT

 

Regression Statistics

 

x) 0

 

.

 

w) Multiple

 

7

 

R

 

7

 

6

 

0

 

ad) R

 

ae)

 

Square

 

al) 0

 

.

 

ak) Adjuste

 

5

 

dR

 

8

 

Square

 

0

 

1

 

ar) Standar

 

as)

 

d Error

 

ay) Observa

 

az) 2

 

tions

 

0

 

bf) ANOVA

 

bg)

 

bm)

 

bn)

 

bt) bu) d

 

f ca) Regress

 

ion l)

 

r) m)

 

s) n)

 

t) o)

 

u) p)

 

v) y) z) aa) ab) ac) af) ag) ah) ai) aj) am) an) ao) ap) aq) at) au) av) aw) ax) ba) bb) bc) bd) be) bh)

 

bo) bi)

 

bp) bj)

 

bq) bk)

 

br)

 

by) Signi

 

fican

 

ce F bl)

 

bs) cf) 5.78

 

008E

 

-05 cg) bv) SS cc) bw) M

 

S bx) F cd) ce) 27.

 

24

 

93

 

74

 

29 ck) cl) cm) cn) cr) cs) ct) cu) cy) cz) da) db) dg) Pval

 

ue dh) Low

 

er

 

95% di) Up

 

per

 

95

 

% dn) 0.5

 

35

 

2 do) 36.8

 

15 dp) 68.

 

51

 

1 du) 5.7

 

88

 

E05 dv) dw) cb)

 

ch) Residua

 

l

 

co) Total

 

cv) dc) dj) Intercep

 

t dq) Size

 

(Square

 

Feet) ci)

 

cp)

 

cw)

 

dd) C

 

o

 

e

 

f

 

f

 

i

 

c

 

i

 

e

 

n

 

t

 

s

 

dk) 1

 

5

 

.

 

8

 

4

 

7

 

9

 

dr) 0

 

.

 

0

 

6

 

9

 

5 cj) 1396

 

0.49

 

cq) 3509

 

4.63

 

cx) bz) df) t

 

de) Stan

 

dard

 

Erro

 

r dl) 25.0

 

665 ds) 0.01

 

33 dx)

 

25) The model predicts that the price of a residential property

 

with a size of 3,000 square feet would be ______ thousand.

 

a) $219

 

b) $224 S

 

t

 

a

 

t dm) 0

 

.

 

6

 

3

 

2 dt) c)

 

d) $230

 

$236 26)

 

27) The standard error of estimate for the regression is: a)

 

b)

 

c)

 

d) 18.565

 

19.941

 

23.554

 

27.849 28)

 

29) The regression sum of squares (SSR) is:

 

a) 1930.605

 

b) 20480.87

 

c) 21134.14

 

d) 24411.48

 

30)

 

31) The regression model estimates that _____% of the variation

 

in the price of the residential properties is explained by the

 

size of the properties.

 

a) 78%

 

b) 72%

 

c) 67%

 

d) 60%

 

32) 33) The value of the test statistic to test the null hypothesis that

 

property size does not influence the price of the property is

 

______.

 

a) 4.128

 

b) 5.226

 

c) 6.425

 

d) 7.921

 

34)

 

35) The margin of error to build a 95% confidence interval for

 

the slope coefficient that relates the price response to each

 

additional square foot is _______.

 

a) 0.028

 

b) 0.042

 

c) 0.051

 

d) 0.063 36)

 

37) 38)

 


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