Statistics Wages and Salaries Questions

Exercise 1A survey of wages and salaries was conducted among 75 farm workers. The margin of error on the
average wage estimated by the survey is ±$2/hr, in 19 out of 20 cases. If we want to increase the
precision of the estimate and have a margin of error of only ±$1/hr in 19 out of 20 cases, how many
workers should be surveyed in total?
Respondents should be “how much” surveyed.
Exercise 2
In Santa’s factory, a machine produces boxes of chocolate candy. Each box contains exactly 100 candies.
On average, the candies weigh 9 grams each, but the exact weight of each candy varies.
The coefficient of variation for the weight of the candy is 12%.
Since you know the statistics, Santa asks you to help him: “Ho! Ho! I know that the average box should
weigh 900 grams. However, there is uncertainty about the total weight of the box because the candies
are not all identical. With 98% confidence, Ho! Ho! what is the margin of error on the weight of a box
containing 100 candies?”
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Your answer will be a margin of error. If you are working on paper, show your approach and give a
complete sentence for the answer.
The boxes weigh 900 g ± “how much” g in 49 of 50 cases.
Exercise 3
A recent study by the Institut de la statistique du Québec revealed that 49% of young Quebecers
surveyed had used cannabis in the past year.
The sample consisted of 562 Quebecers between the ages of 18 and 24, randomly selected from the
population.
In 19 cases out of 20, what percentage of young Quebecers have smoked cannabis in the past year?
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Your answer will be a margin of error. If you are working on a piece of paper, show your approach and
give a complete sentence for the answer.
The survey suggests that 49% of youth have smoked cannabis in the past year. The margin of error on
this survey result is ± “how much” % in 19 out of 20 cases.
Exercise 4
In deciding whether to continue studying, Tiago wonders if the years spent in school help him find a job.
He looks at a study that compares the experiences of 5 people with different levels of education who
looked for work during a period of unemployment. Here is a table that summarizes the number of years
spent in school and the number of days spent looking for work for each person.
Alex
Bea
Charles
Denley
Erika
10
13
12
16
21
Days of unemployment 48
59
31
35
75
Years in school
A) How large is the correlation coefficient that describes the strength of the relationship between years
of schooling and days of unemployment, and what does it mean?
B) Knowing that Tiago has 17 years of schooling, use linear regression to estimate the time he will spend
unemployed.
Statistically, using linear regression, we estimate that Tiago will spend “how much” days unemployed.
Exercise 5
Here is a table from the Institut de la statistique du Québec that shows the spouses married in 2019
whose education level is known (data from ISQ, for heterosexual marriages):
Distribution of marriages by education of spouses, Quebec, 2019
Wife’s last successful level of education
Husband’s last level of education
Less than high school High
school College University
Less than secondary
282
441
183
96
Secondary
240
3,777
1,685
1,435
College
48,
868
1,833
1,699
University
25
,573
1,103
5,349
Using this table as a sample, determine whether there is statistical independence or statistical
dependence between the wife’s and husband’s education levels at the 1% significance level.
What are your null and alternative hypotheses for this chi-square test?
What is the calculated chi-square? Chi-square is “Answer”
Which hypothesis do you retain and what are your conclusions?