Math 155 Practice Final Exam Questions
1. For a class of 140 students, scores on a recent exam (on a scale from 0 to 100) were as follows:
Score / 90-100 / 80-89 / 70-79 / 60-69Relative Frequency / .15 / .25 / .35 / .10
What is the frequency of a score between 0 and 59?
a. .15
b. .85
c. 0
d. 21
e. 30
2. The statistics x=25, s2=16 are computed from sample data from a population.
What is the z-score for an observation: x=9?
a. 1
b. -1
c. 4
d. -4
e. None of the above
3. For a sample of 25 observations, the sum of all observations is 455 and the sum of all squared observations is 16,057.
The sample standard deviation is equal to which of the following?
a. 16
b. 18
c. 25.6
d. 256
e. 324
4. If a balanced die is rolled twice, the probability that both rolls are the same is equal to which of the following?
a. 1/36
b. 2/36
c. 1/6
d. 2/6
e. None of the above
The box plots below are for the reaction time (in seconds) from a study of 100 subjects where 50 were subjected to a non-threatening stimulus (NT) and the other 50 were subjected to a threatening stimulus (T).
Questions 5 and 6 below refer to the box-plots above.
5. What percentage of the subjects who received a threatening stimulus had reaction times exceeding 1.8 seconds?
a. 0%
b. 25%
c. 50%
d. 75%
e. 100%
6. Which of the following statements is incorrect?
a. The inter-quartile range for the group who received a non-threatening stimulus was .3 seconds.
b. The twenty-fifth percentile of reaction times for those who received a non-threatening stimulus was greater than the seventy-fifth percentile for those who received a threatening stimulus.
c. The difference in median reaction times for the two groups is .3 seconds.
d. In all of the data there was only one outlier.
e. The reaction times for the 50 subjects who received the threatening stimulus were from a low of 1.3 seconds to a high of 2.1 seconds.
Questions 7-9 refer to the stem and leaf diagram below.
The stem and leaf diagram below is for EPA gas mileage (MPG) data for a sample of 80 Honda CRV’s (model year 2008) that were tested for fuel efficiency. In this figure, a mileage of 30.0 would have a stem of 30 and a leaf of 0 (representing the fractional part of a mile per gallon).
You are also given for this data the following summary statistics:
i=180xi = 2,968.3 and i=180xi2 = 109,794
Stem-and-leaf of MPG N = 80
Leaf Unit = 0.10
1 30 0
2 31 8
5 32 579
9 33 1269
13 34 2489
21 35 13566789
38 36 00123344556677889
(18) 37 001112233445667789
24 38 22345678
16 39 00347
11 40 02557
6 41 002
3 42 1
2 43 2
1 44 9
7. Determine the median mileage for this sample.
a. 36.95
b. 37.00
c. 37.05
d. 37.10
e. 37.15
8. Determine the mean mileage to the nearest .01 mile per gallon for this sample.
a. 29.68
b. 36.95
c. 37.00
d. 37.05
e. 37.10
9. Determine the percentage of cars in the sample whose MPG rating met or exceeded 39 miles per gallon.
a. 14%
b. 16%
c. 18%
d. 20%
e. 22%
10. In a gambling game, two different numbers are selected at random from the whole numbers 1, 2, 3, … , 10 to form the “winning” combination. You play the combination 1 and 3.
The probability that you will win is:
a. 1/10
b. 4/10
c. 1/90
d. 1/45
e. 1/100
Use the following information for questions 11-13.
The outcome for rolling a pair of balanced dice is the sum of the dots on the upward faces. The probability model for the different outcomes is:
Sum / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12Probability / 1/36 / 2/36 / 3/36 / 4/36 / 5/36 / 6/36 / 5/36 / 4/36 / 3/36 / 2/36 / 1/36
Events: A=7 ≤sum ≤12 , B= 6 ≤sum ≤8
11. Determine the probability that event A will not occur.
a. 5/12
b. 5/11
c. 6/11
d. 6/12
e. 7/12
12. Determine the probability that event A occurs, given that event B occurs.
a. 11/16
b. 11/21
c. 11/36
d. 16/36
e. 21/36
13. Determine the probability that event A occurs, or event B occurs, or both events occur.
a. 11/36
b. 15/36
c. 21/36
d. 26/36
e. 37/36
14. An experiment has 3 possible outcomes denoted by . Which of the following is the probability missing in the table below?
Outcome / / /Probability / .24 / .33
a. .33
b. 33
c. .43
d. 43
e. It cannot be determined without additional information.
15. The probability that event E occurs, or event F occurs, or that both E and F occur is .60. The probability that event E occurs is .48. The probability that event F occurs is .57.
Determine the probability that both events E and F occur.
a. .03
b. .09
c. .12
d. .45
e. 1.05
16. X is a discrete random variable with .
The mean value of X is _____.
a. 1.0
b. 1.5
c. 2.0
d. 2.7
e. 3.0
17. X is a discrete random variable with .
The standard deviation of X is _____.
a. 0.450
b. 0.671
c. 1.000
d. 1.643
e. 2.700
18. A fair coin is flipped 5 times. Determine the probability that at least 4 heads occur in the 5 flips.
a. 1/32
b. 4/5
c. 6/32
d. 26/32
e. 31/32
19. For an adult population, the average weight is 188 pounds and the standard deviation is 12 pounds. The weights for this population are normally distributed. You randomly select 4 of these adults and compute the average value: X.
Determine the probability that X exceeds 194.
a. .1587
b. .1915
c. .3085
d. .3413
e. Cannot be determined.
20. A balanced die is rolled 20 times. On average, the number of “sixes” that you roll is equal to _____.
a. 3
b. 10/3
c. 6
d. 10
e. Cannot be determined since the number of sixes rolled is random.
21. An unbalanced die is manufactured so that there is a 20% chance of rolling a “six.” The die is rolled twenty times. The probability of rolling at least 4 “sixes” is equal to ______.
a. .370
b. .411
c. .589
d. .630
e. .800
22. If is normally distributed with mean 84 and variance 9, then PX<75= _____.
a. .0001
b. .0013
c. .1587
d. .3413
e. .9999
23. The statistics x=25, s2=16 are computed from sample data from a population.
What observation x corresponds to a z-score -.5?
a. 17
b. 19
c. 21
d. 23
e. 27
24. Thirty subjects are selected at random from a population of adult males. In this group, 20% of the population is at least 40% over their “desirable” weight. X is the number of males in this sample who are at least 40% over their “desirable” weight.
Which of the following describes the probability distribution of the random variable X?
a. X is approximately normal with mean 6.
b. X is approximately normal with mean 12.
c. X is binomial with mean 6.
d. X is binomial with mean 12.
e. None of the above statements is true.
25. Two hundred and fifty-six subjects are randomly selected from a population of adult males. The average weight for this population is 192 pounds and the standard deviation is 16 pounds. X is the average weight for this sample.
Which of the following statements is correct?
a. The random variable X- 19216 has a distribution that is approximately standard normal.
b. The random variable X- 1924 has a distribution that is approximately standard normal.
c. The random variable X- 1921 has a distribution that is approximately standard normal.
d. The random variable X- 1921/4 has a distribution that is approximately standard normal.
e. The random variable X- 1921/16 has a distribution that is approximately standard normal.
26. The random variable has mean 72 and variance 36.
For a sample of size from this population, calculate the z-score of a sample mean equal to 73.
a. .17
b. .67
c. 1.00
d. 1.33
e. 1.50
27. Which statement regarding the sampling distribution of the sample mean X is incorrect?
a. On average, the sample mean is equal to the population mean.
b. The standard deviation of the sample mean is equal to the standard deviation of the population divided by the sample size.
c. The distribution of the sample mean is approximately normal if the sample size is sufficiently large.
d. The t-distribution is not appropriate for approximating the distribution of the sample mean.
e. The mean and variance of the sample mean can be determined from the mean and variance of the population together with the sample size.
28. For a random variable X, the standard deviation is σX=10.
How large a random sample is required to make the standard error of the mean equal to .1?
a. 10
b. 100
c. 1,000
d. 10,000
e. 100,000
29. Which of the following statements regarding the large-sample (i.e. n≥30), 95% confidence interval for a population mean is incorrect?
a. If the sample size is quadrupled, then the width of the interval is halved.
b. The width of the interval is 1.96 times the standard error of the mean.
c. The midpoint of the interval is the sample mean, a point estimator of the population mean.
d. In repeated use of this procedure, there is a 95% chance that the true mean will be contained in the confidence interval
e. The value of α is .05.
30. A small sample t-test is conducted to test the null hypothesis μ=30 against the alternative that the population mean exceeds 30. The population is normally distributed. For a sample of size 16 the value of the test statistic is 2.125.
Which of the following statements is correct?
a. The null hypothesis is rejected at a 20% level of significance, but it is not rejected at a 10% level of significance.
b. The null hypothesis is rejected at a 10% level of significance, but it is not rejected at a 5% level of significance.
c. The null hypothesis is rejected at a 5% level of significance, but it is not rejected at a 2.5% level of significance.
d. The null hypothesis is rejected at a 2.5% level of significance, but it is not rejected at a 1% level of significance.
e. The null hypothesis is rejected at a 1 % level of significance, but it is not rejected at a .5% level of significance.
31. For a sample of size 16 randomly selected from a normal population, the sample standard deviation is 8.
Determine the sampling error with a confidence level of 98%.
a. 1.301
b. 2.583
c. 2.602
d. 5.166
e. 5.204
32. For a large sample, 2-sided, Z-test about a population mean, the p-value associated with the statistic value Z=1.54 is ______.
a. .0618
b. .0813
c. .1236
d. .4382
e. .8764
33. For a large sample, 1-sided, Z-test about a population mean where the alternative hypothesis is: Ha: μX< μ0, the p-value associated with the statistic value Z=-2.26 is ______.
a. -.0119
b. .0119
c. .0122
d. -.4881
e. .4881
34. From sample data for a sample of size 50, a 97% confidence interval for a population mean is determined to be equal to 54.2 , 57.6.
Which of the following statements is false?
a. The probability that the interval 54.2 , 57.6 contains the true population mean is .97.
b. The value of the sample mean for this set of data is 55.9.
c. The sampling error is 1.7.
d. We are highly confident that the population mean is at most 57.6.
e. The zα/2 value used in computing this interval is 2.170.
35. For any hypothesis test, which of the following are true?
I. The level of significance is equal to the probability of a type I error.
II. The level of significance is equal to the probability that the null hypothesis is accepted when in fact the alternative hypothesis is true.
III. The level of significance is equal to the probability that the test statistic falls in the rejection region.
a. Only statement I is true.
b. Only statement II is true.
c. Only statement III is true.
d. Only statements I and II are true.
e. Only statements I and III are true.
36. Which of the following statements concerning the probability that a random variable X falls within the interval μX ±1.50σX is correct?
a. The probability is equal to P(-1.50 ≤ Z≤1.50) where Z is a standard-normal, random variable.
b. The probability is midway between .68 and .95.
c. The probability is between 4/9 and 5/9.
d. The probability is midway between 5/9 and 3/4.
e. The probability is at least 5/9.
37. A 95% confidence interval for the proportion of voters favoring a certain ballot measure is computed as .48402 , .54598 for a sample of 1,000 voters.
Determine the number of voters in the sample who favored this ballot proposition.
a. 510
b. 515
c. 520
d. 525
e. 530
38. A 95% confidence interval for the proportion of voters favoring a certain ballot measure is computed as .48904 , .55096 from a sample of 1,000 voters.
Which of the following statements is correct?
a. It has been proven that more than 50% of voters are in favor of this ballot measure.
b. With 95% confidence, we know that at least 50% of the voters are in favor of this ballot measure.