# Statistics 4 1. Grade point averages of math majors at a large distance education university are…

Statistics
4

point averages of math majors at a large distance education
university
are normally distributed with a mean Âµ = 2.85 and a standard
deviation of.png”> = 0.30. If a random
sample of 25 majors is selected from
that university, what is the
probability that the sample mean grade point
will be

a.
either
less than 2.709 or more than 2.955

b.
at
least 2.757 ?

2.
Psychologists estimate that 80% of male drivers, when lost in trying to
find
a location, continue to drive rather
than asking for directions. If this
estimate is correct, what is the
probability that in a random sample of 100
lost male drivers, the proportion who
continue to drive is

a.
at
least 0.70?

b.
less
than 0.85?

3.
A researcher wishes to estimate the mean age of all runners who
participate
in the annual Vancouver marathon. A
random sample of 36 participants indicated
a mean age of 31.4 years. It is known
that the population standard deviation of the
ages is.png”> = 7.2 years.

a.
Construct
a 97% confidence interval for the population mean age.
Note: Express
the confidence interval to 2 decimal places of accuracy.

4.
A random sample of representatives from seven companies was interviewed
in order to find the number of
computers they plan to order next year.
The result are shown below.

8 15 33 10
9 25 12

Assuming that the population of number of computers planned to be
ordered next

year is normally distributed, construct a 95% confidence interval for
the population

mean.

Note: Express the confidence interval to 2
decimal places of accuracy.

5. A survey is being planned to estimate,
with a 98% confidence interval, the
mean amount of time per week that
seniors spend watching television. The
population standard deviation is
known to be 5.2 hours. What sample size will
be required to obtain an estimate
that is within 0.5 hours of the population mean?

6. A survey was conducted to determine the
percentage of students at a post-
secondary institution who prefer
the new alpha-grading system. The responses
from a random sample of 30 students
are shown below.

Yes No
Yes Yes No
Yes
No Yes
Yes No Yes
No
Yes No
Yes No Yes
Yes
Yes Yes
No Yes No
No
No Yes
Yes No Yes
Yes

Construct a 98.5% confidence
interval for the population proportion who
prefer the new alpha-grading
system.

Note:Express
the confidence interval to 4 decimal places of accuracy.

7. A researcher wishes to estimate the
proportion of eligible voters who will vote
for a particular candidate in an up
coming election.

a.
How
large should the sample size be so that a 85% confidence interval for
the
population proportion has a margin of error of 0.05? Assume that a preliminary
sample suggests the proportion is 0.65.

b.
Assuming
that the results of a preliminary surveys are not available,
what is the
most conservative estimate of the sample size that would limit the margin of
error to within 0.05 of the population proportion for an
95% confidence interval?

8. A study conducted last year indicated that
adults spent an average of 14 hours
on household chores during the weekend.
A research group wishes to determine
if the average hours spent on household
chores during the weekend this year is
different from the 14 hours of last
year. Consequently, the research group selects
a random sample of 64 adults and finds
the mean hours spent on household chores
during the weekend to be 15.05 hours.
The population standard deviation is
known to be 3.0 hours.

a.
Formulate
and test the appropriate hypotheses using the P-value approach. What is the
p-value of the test? Would you reject the null hypothesis at
.png”> = 0.01? What would be

b.
Would
you reject the null hypothesis at.png”>=0.001? What would be your
conclusion?

c.
How
strong is the evidence against H.png”>?

9.
A psychologist believes that if classical music is played during a test,
test scores
will increase. In the past, the mean
test score was 60. A random sample of 49
individuals wrote the test while
classical music was in the background. The sample
results showed a mean test score of 62
and a standard deviation of 6.3. Using a 5%
level of significance, can the
Psychologist conclude that the mean test score has
increased with classical music?
Formulate and test the appropriate hypotheses.
Use the critical value approach.

10. A telephone company estimates that 30% of
its customers are interested in
high-speed internet service. To test
this estimate, a random sample of 100
customers was selected and the
results showed that 25% was interested in

high-speed internet
service. Can it be concluded that the percentage of customers
interested in high-speed internet
service is different from 30%? Formulate
and
test the appropriate hypotheses at a
5% significance level. Use the critical value
approach.