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Economics
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Jun 23, 2024
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Technology Notes for lesson 11.4 – Hypothesis Testing: Two Population
Proportions
Question (1)
A Gallup poll to survey the top concerns of Americans was conducted. Suppose that 399 women
and 456 men were independently and randomly selected and that 223 women and 198 men chose the state of the economy as their biggest concern. Can we conclude that the proportion of women (
p
¿¿
1
)
,
¿
choosing the state of the economy as their biggest concern, exceeds the proportion of men (
p
2
)
? Use a significance level of α
=
0.05
for the test. Step 1 of 6
State the null and alternative hypotheses. H
0
:
p
1
p
2
H
a
:
p
1
p
2
Correct Answer: H
0
:
p
1
−
p
2
=
0
; H
a
:
p
1
−
p
2
>
0
Step 2 of 6
Find the value of the two sample proportions,
^
p
1
∧
^
p
2
. Round your answer to three decimal places.
.
Correct Answer: ^
p
1
=
0.559
∧
^
p
2
=
0.434
Step 3 of 6
Compute the weighted estimate of p,
p
. Round your answer to three decimal places. Correct Answer: p
=
0.492
Step 4 of 6
Compute the value of the test statistic. Round your answer to two decimal places. Correct Answer: 3.64
Step 5 of 6
Find the P
-value for the hypothesis test. Round your answer to four decimal places. Correct Answer: 0.0000
Step 6 of 6
Make the decision to reject or fail to reject the null hypothesis. o
Fail to reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men. o
Fail to reject the null hypothesis. There is not sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men.
o
Reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men.
o
Reject the null hypothesis. There is not sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men.
Correct Answer: Reject the null hypothesis. There is sufficient evidence, at the 0.05 level of significance, that the proportion of women choosing the state of the economy as their biggest concern exceeds the proportion of men.
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Related Questions
“Business Ethics is the application of ethical and moral principles or in a business environment. It deals with what is right and what wrong while doing business”. But to the contrary, evidences show that some business organizations are involved in different unethical practices to increase their profit at the risk of many people’s money, health and lives. As a business ethics student you are required to address the following questions:
Describe five unethical practices adopted by business organizations in Oman. You may find it form newspapers, magazines etc. or from your own experiences and observation if any. And Analyze each of these unethical practices and explain how these unethical practices affect the people and society as a whole. And Suggest the ways to overcome each of these unethical practices.
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2. Based on past records, it is generally believed that on an average, a typical University of Technology and Applied Sciences, Nizwa student spends about 25 hours in the LRC per week. Recently, the library has been shifted to a new location which is further away from the academic block. As a result, the administration feels that students may be spending less time in the library. Accordingly a random sample of 41 students were selected and the average number of hours they spend in the library came out to be 16.78 with a standard deviation of 5.17. Carry out an appropriate test of hypotheses for the above problem to test whether the shifting of the library has adversely impacted the study time in the population of all students. (You may assume that study times/week approximately follow a normal distribution in the population).
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Problem is given:
Out of a total number of 10,000 candidates who
applied for jobs in a government department,
6,854 were males, 3,146 were graduates and
others, non-graduates. The number of
candidates with some experience was 2,623 of
whom 1,860 were males. The number of male
graduates was 2,012. The number of graduates
with experience was 1,093 that includes 323
females?
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7.
Some years ago, a new brand of toothpaste was introduced in the United States. According to its
advertisements, studies showed that it had "considerable success" in improving the health of a
person's teeth. Suppose that these studies were designed in the following way. The
manufacturer of this toothpaste chose three samples of seven people; the first sample agreed to
use the new brand, the second sample used Brand A, and the third sample used Brand B. After
six months, a dentist examined each person's teeth and scored the health of his or her teeth on
a scale of 0 (lowest possible score) to 100 (highest possible score). The results were as follows:
New Brand
Brand A
Brand B
65
58
54
71
60
38
53
63
43
55
90
61
34
95
94
82
89
96
77
62
82
The manufacturer of the new toothpaste says that the average score for the new brand is 2
points higher than for Brand A and 4 points higher than for Brand B. Would you agree with the
manufacturer's advertisements? Explain.
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A CBS News poll involved a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.
If we randomly select one of the adults who participated in this study, compute: (round to four decimal places)a.P(affiliated with neither party) = b.P(better) = c.P(better|affiliated with neither party) = d.P(affiliated with neither party|better) = e.P(affiliated with neither party and better) =
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Question:
In two large populations, there are 30 and 25
per cent respectively of blue-eyed people. Is
this difference likely to be hidden in samples
of 1,200 and 900 respectively from the two
populations ?
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Об.
A survey was conducted in which 100 males and, independently, 100 females were asked
about their respective methods of transportation to work. Participants were asked whether they
typically drive to work, use public transportation, or walk / bicycle. The results are given in the
table below. Can the investigators conclude that males differ from females in their work
commute tendencies? Show your work.
Drive Public Transportation Walk or Bicycle
22
Females 71
Males
76
18
6
(a) Based on the assumption that female and male tendencies are alike, construct a table of
expected frequencies.
(b) Use a X² test to evaluate the assumption used in part a. Make sure you indicate which
test you are using!
(c) Interpret the result of part b in terms of the situation of the problem, without using any
statistical language.
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habits if they first experience alcohol in a controlled environment. Other parents take a strict no-drinking approach. Researchers surveyed a sample of 200 students
aged 14 to 17, about their alcohol use and about alcohol related problems. Using a=0.05, answer the questions
No Alcohol related Problems
Alcohol Related Problems
Not allowed to drink
71
9
80
Allowed to drink
89
31
|120
160
40
N=200
What is the alternative hypothesis? [ Select]
What is the null hypothesis? [ Select]
What inferential test is being conducted? [ Select]
What is the obtained statistic? [ Select ]
What determines the critical value? [ Select ]
What is the critical value? [ Select ]
What is the decision rule? [ Select]
What is your decision? [ Select]
What is your conclusion? [ Select ]
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among 2,000 individuals.
i. What is the population for this survey?
ii. What constitutes the sample?
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Smoked 6-10 cigarettes per day --- 10.3% developed asthma
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In order to study the relationship between the number of cigarettes smoked by pregnant women per day and the
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Percentage of children developed asthma
What is the value of the correlation coefficient?
Г
15-5 30.5…
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children
Sunday
adults
children
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