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

Statistics

4

1. Grade

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

your conclusion?

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.

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