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Answered: - Assignment 5A Total Marks = 88 Please show all your work. Some
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May I please get some help at least with these two assignments?instead of 3 --only 2assisngments.?
Assignment 5A
Total Marks = 88
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Question 1
A researcher is comparing the reaction times of 10-year-olds who
play video games and 10-year-olds who do not. Random samples
from each group provided the results shown below.
Reaction times of 10-year-olds
Players of
Video
Games
Sample size
Non-players
of Video Games
15
10
Mean reaction
time
(seconds)
0.50
0.52
Standard deviation
of reaction times
(seconds)
0.01
0.02
Assume that the reaction times for both populations are normally
distributed with the same population standard deviation.
7 marks
a. Construct a 98% confidence interval for the difference
between the population means of reaction times.
Note: Express your answer to 5 decimal places of accuracy.
Introduction to Statistics
1
8 marks
2
b. Using a 2.5% significance level, can the researcher conclude
that the mean reaction time of players of video games is less
than the mean reaction time of non-players of video games?
Formulate and test the appropriate hypotheses. Use the
critical value approach.
Mathematics 215 / Assignment 5A
Question 2
Is there any difference between the proportion of Americans who
wish they were rich and the proportion of Canadians who wish
they were rich? A random sample of 1,000 Americans showed that
550 wish they were rich, while a random sample of 500 Canadians
showed that 225 wished they were rich.
6 marks
a. Find a 97.5% confidence interval for the difference between
the population proportions who wish they were rich.
Note: Express your answer to 4 decimal places of accuracy.
Introduction to Statistics
3
9 marks
4
b. Test, at the 1% level of significance, whether the two
population proportions are significantly different. Formulate
and test the appropriate hypotheses. Use the critical value
approach.
Mathematics 215 / Assignment 5A
Question 3
A motivational program was designed to increase the number of
hours each student who took it studied per week. Eight randomly
selected students were involved in the program. The table below
shows the number of hours each student studied per week before
the taking motivational program and after taking the program.
Before program
After program
8
12
10
12
5
10
10
12
12
11
14
15
8
15
9
6
11 marks At the 10% level of significance, can it be concluded the
motivational program increased the average number of hours
students studied per week? Formulate and test the appropriate
hypotheses. Use the critical value approach.
Assume that the population of paired differences has a normal
distribution.
Introduction to Statistics
5
Question 4
It has been hypothesized that the distribution of seasonal colds in
Canada is as follows:
Season
Percentag
e
Fall
35%
Winter
25%
Spring
30%
Summer
10%
A random sample of 200 Canadian citizens provided the following
results:
Season
Observed
Frequency
Fall
80
Winter
40
Spring
70
Summer
10
10 marks Do the observed data contradict the hypothesis? Formulate and
test the appropriate hypotheses at the 5% level of significance.
Use the critical value approach.
6
Mathematics 215 / Assignment 5A
Question 5
A large company is interested in knowing whether there is any
relationship between a person?s age and that person?s opinion
about a new wage incentive plan. A random sample of 100
employees was selected and cross-classified as shown below.
Opposed
Opinion
Neutral
In Favour
Under 35
35 to 55
Over 55
5
10
15
5
30
10
10
10
5
10 marks At the 1% level of significance, can it be concluded that there is a
relationship between an employee?s age and an employee?s
opinion about the new wage incentive plan? Formulate and test
the appropriate hypotheses. Use the critical value approach.
Introduction to Statistics
7
Question 6
A random sample of 16 students showed that the variance in the
number of hours they spend studying for a final exam was 25
hours2.
7 marks
8
a. Construct a 95% confidence interval for the population
variance and standard deviation of hours spent studying.
Assume the population of hours spent studying is normally
distributed.
Mathematics 215 / Assignment 5A
8 marks
Introduction to Statistics
b. Test, at the 5% level of significance, whether the population
standard deviation of hours spent studying is less than 10. Use
the critical value approach.
9
Question 7
Three different brands of pain relief medication are available for
minor aches and pains. It is of interest to know whether the mean
time to relieve the pain differs from brand to brand. To find out,
twelve individuals with minor aches and pains were randomly
assigned to one of the three brands. The time to relieve the pain
(in minutes) for each individual is provided in the table below.
Brand A
Brand B
Brand C
10
15
20
12
22
25
15
25
20
14
19
11
12 marks Given that the necessary assumptions are satisfied, can it be
concluded, at the 2.5% level of significance, that not all mean
times to relieve pain are equal? Formulate and test the
appropriate hypotheses. Use the critical value approach.
10
Mathematics 215 / Assignment 5A
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