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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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