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Answered: - Assignment 5A Total Marks = 88 Please show all your work. Some


Hello,

May I please get some help at least with these two assignments?instead of 3 --only 2assisngments.?


Assignment 5A

 

Total Marks = 88

 

Please show all your work. Some questions require you to use

 

graphs, tree diagrams, formulas, and so on that are difficult or

 

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submitting is legible.

 

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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