How often do you go out dancing? This question was asked by a professional surve
ID: 3312713 • Letter: H
Question
How often do you go out dancing? This question was asked by a professional survey group on behalf of the National Arts Survey. A random sample of 95 single men showed that 24% went out dancing occasionally. Another random sample of 92 single women showed that 21% went out dancing occasionally. Is the proportion of single men who go out dancing occasionally higher than the proportion of single women? Use a 5% level of significance.
If group 1 is men and group 2 is females, what is the correct alternative hypothesis?
How often do you go out dancing? This question was asked by a professional survey group on behalf of the National Arts Survey. A random sample of 95 single men showed that 24% went out dancing occasionally. Another random sample of 92 single women showed that 21% went out dancing occasionally. Is the proportion of single men who go out dancing occasionally higher than the proportion of single women? Use a 5% level of significance.
If men are group 1 and women are group 2, what is the critical value for this hypothesis test?
A company institutes an exercise break for its workers to see if it will improve job satisfaction as measured by a questionnaire that assesses workers’ satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exercise program are shown in the table below.
Worker
Job Satisfaction Index
Number
Before
After
1
34
33
2
28
36
3
29
50
4
45
41
5
26
37
6
27
41
7
24
39
8
15
21
9
15
20
10
27
37
Does this exercise break improve job satisfaction?
What is the correct alternative hypothesis for this test?
A company institutes an exercise break for its workers to see if it will improve job satisfaction as measured by a questionnaire that assesses workers’ satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exercise program are shown in the table below.
Worker
Job Satisfaction Index
Number
Before
After
1
34
33
2
28
36
3
29
50
4
45
41
5
26
37
6
27
41
7
24
39
8
15
21
9
15
20
10
27
37
Does this exercise break improve job satisfaction?
What is the correct critical value for this hypothesis test?
A company institutes an exercise break for its workers to see if it will improve job satisfaction as measured by a questionnaire that assesses workers’ satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exercise program are shown in the table below.
Worker
Job Satisfaction Index
Number
Before
After
1
34
33
2
28
36
3
29
50
4
45
41
5
26
37
6
27
41
7
24
39
8
15
21
9
15
20
10
27
37
Does this exercise break improve job satisfaction?
What is the p-value for this hypothesis test?
Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of 1 cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results are given in the table below. Assume the distribution to be approximately normal. Do carpeted rooms have more bacteria than uncarpeted rooms?
Carpeted Rooms
Uncarpeted Rooms
11.7
12.0
8.2
8.3
7.1
3.8
13.1
7.3
10.6
12.0
10.1
11.1
14.8
10.3
14.0
13.7
What is the critical value for this hypothesis test if group 1 is the carpeted rooms and group 2 is the uncarpeted rooms.
Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of 1 cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results are given in the table below. Assume the distribution to be approximately normal. Do carpeted rooms have more bacteria than uncarpeted rooms?
Carpeted Rooms
Uncarpeted Rooms
11.7
12.0
8.2
8.3
7.1
3.8
13.1
7.3
10.6
12.0
10.1
11.1
14.8
10.3
14.0
13.7
What is the decision for this hypothesis test if group 1 is the carpeted rooms and group 2 is the uncarpeted rooms.
How often do you go out dancing? This question was asked by a professional survey group on behalf of the National Arts Survey. A random sample of 95 single men showed that 24% went out dancing occasionally. Another random sample of 92 single women showed that 21% went out dancing occasionally. Is the proportion of single men who go out dancing occasionally higher than the proportion of single women? Use a 5% level of significance.
If group 1 is men and group 2 is females, what is the correct alternative hypothesis?
How often do you go out dancing? This question was asked by a professional survey group on behalf of the National Arts Survey. A random sample of 95 single men showed that 24% went out dancing occasionally. Another random sample of 92 single women showed that 21% went out dancing occasionally. Is the proportion of single men who go out dancing occasionally higher than the proportion of single women? Use a 5% level of significance.
If men are group 1 and women are group 2, what is the critical value for this hypothesis test?
A company institutes an exercise break for its workers to see if it will improve job satisfaction as measured by a questionnaire that assesses workers’ satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exercise program are shown in the table below.
Worker
Job Satisfaction Index
Number
Before
After
1
34
33
2
28
36
3
29
50
4
45
41
5
26
37
6
27
41
7
24
39
8
15
21
9
15
20
10
27
37
Does this exercise break improve job satisfaction?
What is the correct alternative hypothesis for this test?
.A company institutes an exercise break for its workers to see if it will improve job satisfaction as measured by a questionnaire that assesses workers’ satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exercise program are shown in the table below.
Worker
Job Satisfaction Index
Number
Before
After
1
34
33
2
28
36
3
29
50
4
45
41
5
26
37
6
27
41
7
24
39
8
15
21
9
15
20
10
27
37
Does this exercise break improve job satisfaction?
What is the correct critical value for this hypothesis test?
A company institutes an exercise break for its workers to see if it will improve job satisfaction as measured by a questionnaire that assesses workers’ satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exercise program are shown in the table below.
Worker
Job Satisfaction Index
Number
Before
After
1
34
33
2
28
36
3
29
50
4
45
41
5
26
37
6
27
41
7
24
39
8
15
21
9
15
20
10
27
37
Does this exercise break improve job satisfaction?
What is the p-value for this hypothesis test?
Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of 1 cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results are given in the table below. Assume the distribution to be approximately normal. Do carpeted rooms have more bacteria than uncarpeted rooms?
Carpeted Rooms
Uncarpeted Rooms
11.7
12.0
8.2
8.3
7.1
3.8
13.1
7.3
10.6
12.0
10.1
11.1
14.8
10.3
14.0
13.7
What is the critical value for this hypothesis test if group 1 is the carpeted rooms and group 2 is the uncarpeted rooms.
Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of 1 cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results are given in the table below. Assume the distribution to be approximately normal. Do carpeted rooms have more bacteria than uncarpeted rooms?
Carpeted Rooms
Uncarpeted Rooms
11.7
12.0
8.2
8.3
7.1
3.8
13.1
7.3
10.6
12.0
10.1
11.1
14.8
10.3
14.0
13.7
What is the decision for this hypothesis test if group 1 is the carpeted rooms and group 2 is the uncarpeted rooms.
Explanation / Answer
i.
Given that,
sample one, x1 =22.8, n1 =95, p1= x1/n1=0.24
sample two, x2 =19.32, n2 =92, p2= x2/n2=0.21
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.24-0.21)/sqrt((0.225*0.775(1/95+1/92))
zo =0.491
| zo | =0.491
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =0.491 & | z | =1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 0.491 ) = 0.31173
hence value of p0.05 < 0.31173,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: p1 = p2
alternate, H1: p1 > p2
test statistic: 0.491
b.
critical value: 1.645
decision: do not reject Ho
p-value: 0.31173
we do not have enough evidence to support the claim that the proportion of single men who go out dancing occasionally higher than the proportion of single women
ii)
Given that,
null, H0: Ud = 0
alternate, H1: Ud > 0
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.833
since our test is right-tailed
reject Ho, if to > 1.833
we use Test Statistic
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = -9.5
We have d = -9.5
pooled variance = calculate value of Sd= S^2 = sqrt [ 1625-(-95^2/10 ] / 9 = 8.96
to = d/ (S/n) = -3.353
critical Value
the value of |t | with n-1 = 9 d.f is 1.833
we got |t o| = 3.353 & |t | =1.833
make Decision
hence Value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > -3.3529 ) = 0.99576
hence value of p0.05 < 0.99576,here we reject Ho
ANSWERS
---------------
c.
null, H0: Ud = 0
alternate, H1: Ud > 0
test statistic: -3.353
d.
critical value: reject Ho, if to > 1.833
decision: Reject Ho
e.
p-value: 0.99576
iii)
Given that,
mean(x)=11.2
standard deviation , s.d1=2.726
number(n1)=8
y(mean)=9.8125
standard deviation, s.d2 =3.1921
number(n2)=8
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.89
since our test is right-tailed
reject Ho, if to > 1.89
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =11.2-9.8125/sqrt((7.43108/8)+(10.1895/8))
to =0.93
| to | =0.93
critical value
the value of |t | with min (n1-1, n2-1) i.e 7 d.f is 1.89
we got |to| = 0.93491 & | t | = 1.89
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:right tail - Ha : ( p > 0.9349 ) = 0.19048
hence value of p0.05 < 0.19048,here we do not reject Ho
ANSWERS
---------------
f.
null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 0.93
critical value: 1.89
g.
decision: do not reject Ho
p-value: 0.19048
we donot have enough evidence to support the claim that carpeted rooms have more bacteria than uncarpeted rooms
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