Question

3.5 - A recent census asked respondents to state the highest level of education that they had received. The responses were 39% High school, 45% TAFE or Undergraduate Degree, 13% Higher Degree and 3% Other.

The mayor of a small country town held a similar survey. Below are observed counts for each of the education levels for 250 respondents from the town: Highest Education Level

Highest education level |
Observed count |

High school |
115 |

Tafe or uni |
105 |

Higher degree |
20 |

Other |
10 |

a) If the counts observed for the town matched that of the census, what would be the expected counts for

each education level?

b) To see if these results are unusual, should you perform a goodness-of-fit test or a test of independence?

c) State your hypotheses.

d) How many degrees of freedom are there?

e) Find *x*^{2} and the P-value.

f) State your conclusion (use α = 0.05) in the context of the question.

Show all working out and dont no technology (ie. spss or excel)

Answer #1

a) The following table is obtained:

Categories |
Observed |
Expected |
(fo-fe)^{2}/fe |

High School | 115 | 250*0.39=97.5 | (115-97.5)^{2}/97.5 =
3.141 |

Tafe or Uni | 105 | 250*0.45=112.5 | (105-112.5)^{2}/112.5 =
0.5 |

Higher degree | 20 | 250*0.13=32.5 | (20-32.5)^{2}/32.5 =
4.808 |

Other | 10 | 250*0.03=7.5 | (10-7.5)^{2}/7.5 =
0.833 |

Sum = | 250 | 250 | 9.282 |

b) we should perform a **goodness-of-fit
test.**

c) Null and Alternative Hypotheses:

H0: p1=0.39, p2=0.45, p3=0.13, p4=0.03

Ha: Some of the population proportions differ from the values stated in the null hypothesis.

d) Degree of freedom = 4-1=3

e) Test statistic:

p-value = CHISQ.DIST.RT(9.282, 3) = **0.0257**

f) p-value < α, **Reject** the null
hypothesis.

There is enough evidence to conclude that the population proportions differ from the values stated in the null hypothesis.

Changes in Education Attainment: According to
the U.S. Census Bureau, the distribution of Highest Education
Attainment in U.S. adults aged 25 - 34 in the year 2005 is
given in the table below.
Census: Highest Education Attainment - 2005
i
1
2
3
4
5
No
High
School
Associate's
Bachelor's
Graduate or
Diploma
Diploma
Degree
Degree
Professional Degree
Percent
14%
48%
8%
22%
8%
In a survey of 4000 adults aged 25 - 34 in the year 2013, the
counts...

Changes in Education Attainment: According to
the U.S. Census Bureau, the distribution of Highest Education
Attainment in U.S. adults aged 25 - 34 in the year 2005 is
given in the table below.
Census: Highest Education Attainment - 2005
i
1
2
3
4
5
No
High
School
Associate's
Bachelor's
Graduate or
Diploma
Diploma
Degree
Degree
Professional Degree
Percent
14%
48%
8%
22%
8%
In a survey of 4000 adults aged 25 - 34 in the year 2013, the
counts...

Changes in Education Attainment: According to
the U.S. Census Bureau, the distribution of Highest Education
Attainment in U.S. adults aged 25 - 34 in the year 2005 is
given in the table below.
Census: Highest Education Attainment - 2005
i
1
2
3
4
5
No
High
School
Associate's
Bachelor's
Graduate or
Diploma
Diploma
Degree
Degree
Professional Degree
Percent
14%
48%
8%
22%
8%
In a survey of 4000 adults aged 25 - 34 in the year 2013, the
counts...

Changes in Education Attainment: According to
the U.S. Census Bureau, the distribution of Highest Education
Attainment in U.S. adults aged 25 - 34 in the year 2005 is
given in the table below.
Census: Highest Education Attainment - 2005
i
1
2
3
4
5
No
High
School
Associate's
Bachelor's
Graduate or
Diploma
Diploma
Degree
Degree
Professional Degree
Percent
14%
48%
8%
22%
8%
In a survey of 4000 adults aged 25 - 34 in the...

4 Changes in Education Attainment: According to the U.S. Census
Bureau, the distribution of Highest Education Attainment in U.S.
adults aged 25 - 34 in the year 2005 is given in the table below.
Census: Highest Education Attainment - 2005 i 1 2 3 4 5 No High
School Associate's Bachelor's Graduate or Diploma Diploma Degree
Degree Professional Degree Percent 14% 48% 8% 22% 8% In a survey of
4000 adults aged 25 - 34 in the year 2013, the...

The comparisons of Scholastic Aptitude Test (SAT) scores based
on the highest level of education attained by the test taker's
parents were provided. A research hypothesis was that students
whose parents had attained a higher level of education would on
average score higher on the SAT. The overall mean SAT math score
was (College Board website, January 8, 2012). SAT math
scores for independent samples of students follow. The first sample
shows the SAT math test scores for students whose parents...

A political scientist wanted to learn whether there is an
association between the education level of registered voters and
his or her political party affiliation. He randomly selected 46
registered voters and ran a Chi-square test of Independence and
Homogeneity in SPSS. The following is the test result from
SPSS:
Education * Party Crosstabulation
Party
Total
Democrat
Republican
Education
College
Count
9
12
21
Expected Count
11.9
9.1
21.0
Grade School
Count
7
2
9
Expected Count
5.1
3.9
9.0...

The College Board provided comparisons of Scholastic Aptitude
Test (SAT) scores based on the highest level of education attained
by the test taker's parents. A research hypothesis was that
students whose parents had attained a higher level of education
would on average score higher on the SAT. The overall mean SAT math
score was 514. SAT math scores for independent samples of students
follow. The first sample shows the SAT math test scores for
students whose parents are college graduates...

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