REVIEW QUESTIONS FOR TEST 3

MATH 115
(TELECOURSE)

COLLEGE OF MARIN

Instructor: N. Psomas

1. There are 20 multiple choice questions on an exam each having responses a, b, c, and d. Only one option per question is correct. If a student guesses the answer to each question, then the probability that he or she gets the question correct is 0.25. If X is the random variable whose values equal the number of questions a student who guesses will answer correctly, then the probability distribution of X is____________

a. Normal

b. Continuous

c. Binomial

d. Skewed to the left

2. There are 20 multiple choice questions on an exam each having responses a, b, c, and d. Only one option per question is correct. If a student guesses the answer to each question, then the probability that he or she gets the question correct is 0.25. A student passes the exam if he/she answers 65% or more of the questions correctly. . If a student guesses on all 20 of the questions, the chance that he/she passes the exam is what?

a. 0.25

b. 13 out of 20

c. 0.0002

d.
0.0050

3. In a certain large population, 40% of households have a total annual income of over $70,000. A simple random sample of size 4 of these households is taken. Let X be the number of households in the sample with an annual income of more than $70,000. What is the mean of X?

a. 28,000

b. 1.6

c. 0.96

d.
2

4. In a certain large population, 40% of households have a total annual income of over $70,000. A simple random sample of size 4 of these households is taken. What is the probability that 2 or more of the households in the survey have an annual income of over $70,000?

a. 0.4000

b. 0.5000

c. 0.5248

d.
0.3456

5. In a certain large population, 40% of households have a total annual income of over $70,000. A simple random sample of size 4 of these households is taken. Let X be the number of households in the sample with an annual income of more than $70,000. What is the standard deviation of X?

a. 0.980

b. 0.960

c. 167.3

d.
$3,000

6. Which of the following is NOT a property of a binomial setting?

a. There are n observations; each one results in
either a success or a failure.

b. The probability of success is the same for
each observation.

c. Observations are independent.

d. The number of
successes in n observations is independent of the probability of
success.

7. The normal distribution is a reasonably good approximation to the binomial distribution provided that what?

a. np £ 10 and n(1-p) £ 10

b. np ³ 10 and n(1-p) £ 10

c. np £ 10 and n(1-p) ³ 10

d. np ³ 10 and n(1-p) ³ 10

8. Twenty percent of all items produced on an assembly line require adjustment. If n = 100 items are sampled at random from the assembly line, what is the approximate probability that more than 25 of them require adjustment?

a. 0.0400

b. 0.1056

c. 0.2500

d.
0.8944

9. In a large population, 46% of the households own VCR's. A Simple Random Sample (SRS) of 100 households is to be contacted and the sample proportion computed. What is the mean of the sampling distribution of the sample proportion?

a. 10

b. 0.00248

c. 0.46

d.
0.050

10. In a large population, 46% of the households own VCR's. An SRS of 100 households is to be contacted and the sample proportion computed. What is the standard deviation of the sampling distribution of the sample proportion?

a. 0.050

b. 0.00248

c. 0.46

d. 10

11. Forty-five percent of people in a population use "Brand XX" toothpaste. A telephone survey is done and 400 people are asked which brand of toothpaste they used most recently. The probability that more than one half used "Brand XX" most recently is?

a. 0.4778

b. 0.0400

c. 0.022

d.
0.4600

12. A community consists of 5800 adults. Twelve percent of these adults are over 55 years of age. A simple random sample of 200 adults is selected for an opinion poll regarding the community. The proportion of adults in the sample who are over 55 years of age is approximately normally distributed with mean 0.12 and standard deviation ___________.

a. 0.0230

b. 0.0005

c. 21.12

d.
0.1056

13. In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. What is the probability that the sample mean IQ is greater than 110?

a. 0.579

b. 0.921

c. 0.421

d.
0.079

14. The distribution of actual weights of 8 oz. chocolate bars produced by a certain machine is normal with mean 8.1 ounces and standard deviation 0.1 ounces. A sample of 5 of these chocolate bars is selected. The probability that their mean weight is less than 8 oz. is what?

a. 0.0125

b. 0.4871

c. 0.1853

d.
0.9873

15. The incomes in a certain large population of college teachers have a normal distribution with mean $35,000 and standard deviation $5,000. Four teachers are selected at random from this population to serve on a salary review committee. What is the probability that their average salary exceeds $40,000?

a. 0.1587

b. 0.0228

c. 0.9772

d.
0.2119

16. You want to compute a 95% confidence interval for a population mean. Assume that the population standard deviation is known to be 10 and the sample size is 50. The value of z* to be used in this calculation is:

(a) 1.645

(b) 2.009

(c) 1.960

(d)
.8289 (e) .8352

17. A sample of 25 seniors from a large metropolitan area school district had a mean Math SAT score of 450. Suppose we know that the standard deviation of the population of Math SAT scores for seniors in the district is 100. Assume the population of Math SAT scores for seniors in the district is approximately normally distributed. What is a 90% confidence interval for m, the true mean Math SAT score of all seniors in the district?

a. 450 ± 7.84

b. 450 ± 32.9

c. 450 ±
39.2

d. 450 ± 1.96

18. A sample of 25 seniors from a large metropolitan area school district had a mean Math SAT score of 450. Suppose we know that the standard deviation of the population of Math SAT scores for seniors in the district is 100. Assume the population of Math SAT scores for seniors in the district is approximately normally distributed. A 90% confidence interval for the mean Math SAT score m for the population of seniors is used. Which of the following would produce a confidence interval with a smaller margin of error?

a. using a confidence level of 95%

b. using
a confidence level of 99%

c. using a sample of 100 seniors

d. using a
sample of only 10 seniors

19. A sample of 100 postal employees found that the average time these employees had worked for the postal service was 8 years. Assume that we know that the standard deviation of the population of times postal service employees have spent with the service is 5 years. A 95% confidence interval for the true mean time m, of times postal service employees have spent with the postal service is what?

a. 8 ± 0.98

b. 5 ± 1.32

c. 5 ± 1.57

d. 8 ± 0.82

20. The distribution of contents of "Jumbo" bags of a certain brand of potato chips is normal with a standard deviation s = 1oz. Construct a 96% confidence interval for the mean content m of a bag based on four bags that where found to contain 31, 33, 30, & 30 ounces of potato chips.

a. (28oz , 32oz)

b. (30oz , 32oz)

c.
(30oz , 33oz)

d. (29oz , 31oz)

21. A sample of 100 postal employees found that the average time these employees had worked for the postal service was 8 years. Assume that we know that the standard deviation of the population of times postal service employees have spent with the service is 5 years. A 90% confidence interval for the true mean time m, of times postal service employees have spent with the postal service, with margin of error ±0.5 is used. The smallest sample size we can take and achieve this margin of error is what?

a. 385

b. 1000

c. 271

d.
100

22. The national mortgage rate for 30 year fixed rate mortgages is 9.2%. A Realtor in a large Midwestern city believes that local mortgage rates are lower than the national average. The Realtor plans to test this by taking a survey of local lending institutions and determining the (sample) mean 30 year fixed mortgage rate. Let m represent the mean 30 year fixed mortgage rate for all lending institutions in the city. What is the alternative hypothesis the Realtor wishes to test?

(a) H_{a} : m = 9.2%

(b) H_{a} :
m ¹ 9.2%

(c) H_{a} :
m > 9.2%

(d) H_{a} :
m < 9.2%

23. A medical researcher is curious if the mean weight m of all college students has changed since 1980. Suppose in 1980 the mean weight was 150 lb. The researcher plans to examine the weights of a sample of college students taken in 1995 to see if the mean weight of all college students has changed in the last 15 years. What is the alternative hypothesis the researcher wishes to test?

(a) H_{a} : m = 150 lb.

(b)
H_{a} : m ¹ 150 lb.

(c) H_{a} : m > 150 lb.

(d)
H_{a} : m < 150 lb.

24. Which of the following would be strong
evidence against the null hypothesis H_{0} in a hypothesis
test?

(a) a very large P-value

(b) a very small
P-value

(c) a large sample size

(d) a small sample size

25. A significance test gives a P-value of .04. From this we can

(a) reject H_{0} with a = .01

(b) reject
H_{0} with a = .05

(c) say that the probability that H_{0}
is false is .04

(d) say that the probability that H_{0}
is true is .04

**The following information is
used for questions 26, 27, and 28**

"Jumbo" bags of a certain brand of potato chips are supposed to contain 32 ounces (2 lb.) of chips. There is some variation from bag to bag because the filling machinery is not perfectly precise. The distribution of contents is normal with mean m and standard deviation s = 1 ounce. An inspector who suspects that the manufacturer is underfilling the bags measures the contents of 4 bags. The results are: 31, 33, 30, & 30 ounces.

26. Is this convincing evidence that the mean contents of "jumbo" bags is less than the advertised 32 ounces? Using test statistic , what is the P-value?

(a) 31

(b) .0228

(c) .1587

(d) .0456

27. At what level of significance do the above data provide enough evidence to reject the null hypothesis?

(a) 1%

(b) 2%

(c) 5%

(d) .05%

28. In the above data, what are the hypotheses being tested?

(a) H_{0} : m = 32 and H_{a} :
m ¹ 32

(b) H_{0} :
m = 32 and
H_{a} : m > 32

(c) H_{0} : m = 32 and H_{a} :
m < 32

(d) H_{0} :
m ¹ 32 and H_{a} :
m = 32

29. I wish to test the hypotheses H_{0}:
m = m_{0} and H_{a}: m ¹ m_{0} based on an SRS of size *n* from a normal
population with unknown mean m and known standard deviation s. I should reject H_{0}
at significance level a = .05 if the value of the z-statistic z satisfies
what?

(a) z ¹1.96

(b) z > 1.645 or z < -1.645

(c) z < -1.96 or z > 1.96

(d) z ¹
1.645

30. A particular model car advertises that it gets 30 miles per gallon in city driving. A consumer group wishes to test if this is true or if the gas mileage is something different than 30 miles per gallon. They purchase a sample of 4 cars from this model, and find the gas mileage of each after 15,000 miles of city driving. The mean gas mileage for these 4 cars is found to be 28.8 miles per gallon. Assume the distribution of city gas mileage for the population of cars is normal with mean m and standard deviation s = 2 miles per gallon. What is the P-value of the test statistic for this test?

a. .1151

b. .2302

c. 10%

d.
5%