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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

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

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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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