Statistics 5 Complete Solution

Question: #8374

Statistics 5

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 provide 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.

a. Construct a 98% confidence interval for the difference between the
population means of the reaction times.

Note: Express your answer to 5 decimal places of accuracy.

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.

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.

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.

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.

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 taking the 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

At the 10% level of significance, can it be conclude that the motivational program increased the average number of hours students studied per week?
Formulate and test the appropriate hypotheses. Use the critical value approach.

Assuming that the population of paired difference has a normal distribution.

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 Percentage.

                       Fall                           80
                       Winter                     40
                       Spring                      70
                       Summer                  10
              __________________________________

           Do the observed data contradict the hypothesis? Formulate and test the
           appropriate hypotheses at the 5% level of significance. Use the critical value
           approach.

5. A new 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.

                                                                       Opinion
                                     Opposed                 Neutral                  In Favour

      Under 35                     5                                5                                 10

       35 to    55                    10                              30                               10

Over 55 15 10 5
____________________________________________________________________________

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.

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 hours.

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.

c. 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.

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 minute) 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

             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.

Solution: #8376

Statistics 5 Complete Solution

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 hypo...