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 impossible to reproduce in word-processing programs, so you will have to print the entire assignment and fill it out and mail it to your tutor. As an alternative to mailing, you might be able to photograph or scan your assignment and submit it through the appropriate drop box. If you do, make sure the material you are 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	Non-players of Video Games
Sample size	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.

8 marks 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.

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.

9 marks 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.

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	8	12	10	12	5	10	10	12
After program	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.

Question 4

It has been hypothesized that the distribution of seasonal colds in Canada is as follows:

Season	Percentage
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.

Question 5

A large company is interested in knowing whether there is any relationship between a persons age and that persons opinion about a new wage incentive plan. A random sample of 100 employees was selected and cross-classified as shown below.

		Opinion
	Opposed	Neutral	In Favour
Under 35	5	5	10
35 to 55	10	30	10
Over 55	15	10	5

10 marks At the 1% level of significance, can it be concluded that there is a relationship between an employees age and an employees opinion about the new wage incentive plan? Formulate and test the appropriate hypotheses. Use the critical value approach.

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 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.

8 marks 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.

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.