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Exam 7: Total score out of 90 points
Name:
There are 100 questions. There are videos or detailed solutions for ~25 of them (bolded #’s in red).
̅ ; Mean & standard deviation of 𝑿
̅
III.B.2: Central Limit Theorem – Meaning; Sampling distribution of 𝑿
1. The Central Limit Theorem is important in statistics because _____________.
A. … for any size sample, it says the sampling distribution of the sample means 𝑥̅ ′𝑠 is approximately normal
B. … for any population, it says the sampling distribution of the sample means 𝑥̅ ′𝑠 is approximately normal,
regardless of the sample size
C. … for a large n, it says the sampling distribution of the sample means 𝑥̅ ′𝑠 is approximately normal, regardless of
the population
D. … for a large n, it says the original population is approximately normal
2. The Central Limit Theorem states that the sampling distribution of the sample means 𝑥̅ ′𝑠 is approximately normal
under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?
A. The sample size must be large (e.g., at least 30).
B. The population size must be large (e.g., at least 30).
C. The population from which we are sampling must be normally distributed.
D. The population from which we are sampling must not be normally distributed.
3. (DLE Video: Sampling Distributions (onlinestatbook.com)) The distribution of a characteristic is negatively skewed.
The sampling distribution of the sample means 𝑥̅ ′𝑠 for large samples, taken from this same distribution, is:
A. Negatively skewed
B. Approximately normal
C. Positively skewed
D. Lognormal
4. The Central Limit Theorem says that the mean 𝜇𝑋̅ of the sampling distribution of the sample means 𝑥̅ ′𝑠 is:
A. Equal to the population mean μ divided by the square root of the sample size n.
B. Close to the population mean μ if the sample size n is large.
C. Equal to the population mean μ.
D. Indeterminable with the information provided.
5. The Central Limit Theorem says that the standard deviation 𝜎𝑋̅ of the sampling distribution of the sample means
𝑥̅ ′𝑠 is:
A. Equal to the population standard deviation σ divided by the square root of the sample size n.
B. Close to the population standard deviation σ if the sample size n is large.
C. Exactly equal to the standard deviation.
D. Indeterminable with the information provided.
6. (DLE Video) The length of time a traffic signal stays green (nicknamed the "green time") at the intersection of 40
& 46 follows a normal probability distribution with a mean of 200 seconds and the standard deviation of 10
seconds. Which of the following describes the derivation of the sampling distribution of the sample means?
A. The means of a large number of samples of size n randomly selected from the population of "green times" are
calculated and their values are plotted.
B. The standard deviations of a large number of samples of size n randomly selected from the population of "green
times" are calculated and their values are plotted.
C. Since the population of "green times" is normally distributed, the mean is the best measurement of center.
D. A single sample of sufficiently large size n is randomly selected from the population of "green times" and its
value is determined.
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III.B.2: Central Limit Theorem – Applications
7. Samples of size n = 25 (assume CLT holds at 25) are selected from a population with mean μ = 40 and standard
deviation σ = 7.5. The mean 𝜇𝑋̅ and standard deviation 𝜎𝑋̅ of the sampling distribution of the sample means 𝑥̅ ′𝑠 are:
A. 1.6, 0.3
B. 8, 1.5
C. 40, 0.3
D. 40, 1.5
8-9. You’re calculating a 90% two-sided confidence interval for the population mean μ of a normal distribution …
8. (DLE Video) … what is the appropriate z-score?
A. 1.64
B. 1.96
C. Not enough info to determine
D. 1.28
9. (DLE Video) … what is the approximate margin of error (not standard error) for this confidence interval given that
you have n = 65 samples and the population variance is σ2 = 11.
A. 0.41
B. 0.68
C. 0.05
D. 0.08
F. 2.24
10. If a 95% confidence interval for mean μ turns out to be [6.5, 8.5], this means that:
A. The probability is 0.95 that X-bar falls between 6.5 and 8.5
B. The probability is 0.95 that X falls between 6.5 and 8.5
C. The probability is 0.95 that the interval (6.5, 8.5) contains μ
D. 4σ = 8.5 – 6.5
11. When determining a confidence interval for mean μ, based on a sample size of n, we know that:
A. Increasing n increases the interval
B. Having to use standard deviation σ instead of n decreases the interval
C. The larger the interval, the more reliable the estimate of µ
D. Increasing n decreases the interval
12. If a sample size of 16 yields an average of 𝑥̅ = 12 with a standard deviation of s = 3, estimate the 95%
confidence interval for the population assuming it is normal distributed.
A. 10.40 < μ < 13.60
B. 10.45 < μ < 13.55
C. 10.53 < μ < 13.47
D. 10.77 < μ < 13.23
13. Which of the following statements is true?
A. Confidence intervals increase in width as the sample size increases
B. Confidence intervals are always symmetrical
C. Confidence intervals for the mean may be independent of the original population distribution
D. Confidence intervals are independent of the sample size
E. Confidence intervals decrease in width for larger standard deviations
14. Which table should be used to determine a confidence interval for the mean when σ is unknown and the sample
size is 10? Assume the population of interest is normally distributed.
A. Z
B. t
C. F
D. χ² (chi-squared distribution)
15. You’re constructing the confidence interval for the population mean using the normal distribution. What sample
size is needed to create a 95% confidence interval with a margin of error of ±0.85 when the population standard
deviation is 1.14.
A. 30
B. 3
C. 7
D. Not Enough Information
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III.B.2: Central Limit Theorem in Control Charts
16. (DLE Video, Ref 1.4) Your company has received the following information about an Xbar/S control chart:
𝑋̿ = 4.241 mm, 𝑠𝑋̅ = 0.565 mm, and n = 5
You decide to estimate the process parameters 𝜇̂ and 𝜎̂ but discover that the original data was lost and all you have
are these 3 numbers. What is the best estimate that can be made of the process parameters under these
circumstances?
A. 𝜇̂ = 4.241 and 𝜎̂ = 0.565
C. 𝜇̂ = 4.241 and 𝜎̂ = 0.253
B. 𝜇̂ = 4.241 and 𝜎̂ = 1.263
D. 𝜇̂ = 1.896 and 𝜎̂ = 1.263
III.B.2: Central Limit Theorem in Hypothesis Testing
17. A test is conducted for H0: μ = 20, with σ = 4. A sample of size 36 has 𝑥̅ = 21.4. The test statistic is:
A. -12.6
B. 0.35
C. 2.1
D 12.6
18. (DLE Video) A test is conducted for H0: μ = 50 vs. Ha: μ > 50. The test statistic is z0 = 2.46. Assuming that the
sample size for this hypothesis test is larger, e.g., n > 30, what is its p‐value?
A. 0.0069
B. 0.0138
C. 0.9931
D. 0.008
19. (DLE Video) If a 99% two-sided confidence interval is constructed to estimate μ with a known σ and a large
sample size n, then the correct approximate critical values for z are …
A. ±1.96
B. ±2.33
C. ±2.58
D. ±1.28
20. A sample of size n = 40 with a sample mean of 𝑥̅ = 8.4 was selected from a population with σ = 1.2. The 95%
confidence interval for μ is approximately:
A. 8.4 ± 1.96 ∙
1.2
√40
B. 8.4 ± 1.65 ∙
1.2
C. 8.4 ± 1.96 ∙
√40
1.2
40
D. 8.4 ± 1.65 ∙
1.2
40
21. A sample is selected from a normally distributed population with μ = 18.6, and the 90% confidence interval is
[16.8, 18.2]. This means
A. An error was made in computation.
B. The wrong confidence level was used.
C. Random sampling used to construct the confidence interval resulted in a usually low sample mean.
D. The true population mean cannot be μ = 18.6.
22. Researchers want to predict the mean length of fish within 0.5 inches at the 95% level. If σ = 1.6, how many fish
are needed?
A. 30
B. 35
C. 40
D. Not enough info to determine
III.B.2: Difference between descriptive and inferential statistics
23. How do descriptive and inferential statistics differ?
A. Descriptive statistics are more computationally sophisticated than inferential statistics.
B. Inferential statistics are more computationally sophisticated than descriptive statistics
C. Descriptive statistics describe data, while inferential statistics attempt to make predictions based on data.
D. Inferential statistics describe data, while descriptive statistics attempt to make predictions based on data.
24. _____________________ statistics consists of generalizing from samples to populations, performing estimations and
hypothesis tests, determining relationships among variables, and making predictions.
A. Mathematical
B. Descriptive
C. Inferential
D. Population
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III.B.2: Difference between descriptive and inferential statistics (continued)
25-28. Determine if the following represent descriptive (D) or inferential statistics (I).
25(a) A prediction has been made that the chance that a person will be robbed in a certain city is 15%.
D
I
(b) From a past study it was found that the APR of a certain credit card averaged 12.83%.
D
I
26(a) Using this product will burn at least 74% more calories.
D
I
(b) The average salary of the graduates of the class of 1980 is $32,500.
D
I
27(a) A professor at RHIT found that over the past 10 years that the average number of students in a class is 22.6
D
I
(b) From last year’s data, the total attendance at RHIT football games was 8,235 people.
D
I
28(a) A recent study showed that eating garlic can lower blood pressure.
D
I
(b) The Senior Citizens who live in Florida have better memories than the ones who live in Texas.
D
I
III.B.2: Population parameters vs sample statistics
29. (DLE Video) (Example in III.C lesson notes) The sodium content (in mg) of n = 48 randomly selected boxes of
organic cornflakes was determined; the mean of this sample data is 132 mg with standard deviation 1 mg. We are
interested in determining whether the true mean sodium content of all such boxes of organic cornflakes is more
than 130 mg.
Population of interest:
Parameter of interest:
Sample:
Sample statistics:
State the null and alternative hypotheses that reflect the question of interest.
30. A market researcher surveys 85 people on their coffee-drinking habits. She wants to know whether people in the
local region are willing to switch their regular drink to something new. What is the sample?
A. People in the local region
B. The 85 people
C. Society at large
D. The market researcher
31. The market researcher analyzes the data and finds that 61% of survey respondents are willing to switch their
regular drink to something new. What is the 61% referred to as?
A. Parameter
B. Statistic
C. Sampling error
D. Standard error
32. Do the following statements contain a parameter (P) or a statistic (S)?
a. The median annual income of all 37 employees at Company X is $42,000.
P
S
b. The average final math exam scores of seniors from High School A have increased from 70% to 78% over the past
decade.
P
S
III.C: Discrete vs Continuous Random Variables
33-35. Determine if each random variable is continuous (C) or discrete (D).
C
D
33(a) A student tracked the number of nervous tics he had per day during Spring Quarter 2010.
C
D
(b)The time required for a mailperson to finish their typical route.
C
D
34(a) Number of medication errors tracked by customers at a given pharmacy.
C
D
(b)Length of the longest pencil in your book bag.
C
D
35(a) Number of potato chips in a bag.
C
D
(b) Number of times my dogs wake me up at night.
C
D
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III.C: Binomial Distribution
36. (DLE Video) (Example in III.C lesson notes) Suppose that 20% of all copies of a particular textbook fail a certain
binding strength test. Let X represent the number of copies that fail the test out of a random sample of size n = 4.
Assuming independence of each book’s binding strength, determine the probability mass function, expected value,
and standard deviation of X.
37. (Example in III.C lesson notes) A nationwide survey showed that 65% of all children in the United States dislike
eating vegetables. Let X represent the number of 10 randomly selected children who dislike eating vegetables.
Determine the probability mass function of X and include its support. (a) What is the probability that exactly 2 of the
10 children dislikes eating vegetables? (b) What is the probability that at least one of the 10 dislikes eating
vegetables?
38. (Example in III.C lesson notes) Suppose that only 25% of all campus drivers come to a complete stop at any of
the stop signs on campus when no other cars are visible. How many of the next 25 drivers do you expect to come to
a complete stop at a campus stop sign when no other car is visible? What’s the standard deviation in the number of
stops?
39. A random sample of n = 600 measurements is drawn from a binomial population with probability of success π =
0.08. Give the mean and the standard deviation of the sampling distribution of the sample proportion, p.
A. 0.08; 0.011
B. 0.92; 0.003
C. 0.08; 0.003
D. 0.92; 0.011
40. ASQ sectional history indicates that 70% of all candidates successfully pass the CSSGB certification exam. A total
of 12 company employees (including you) will take the upcoming CSSGB exam. The area manager has promised a
big bonus if all 12 of you pass the exam. What is the probability of getting the promised bonus?
A. 0.700000
B. 0.083000
C. 0.013841
D. 0.001176
41. The real estate industry claims that it is the best and most effective system to market residential real estate. A
survey of randomly selected home sellers in Illinois found that a 95% confidence interval for the proportion p of
homes that are sold by a real estate agent is [69%, 81%]. Interpret the interval in this context.
A. In 95% of the years, between 69% and 81% of homes in Illinois are sold by a real estate agent.
B. 95% of all random samples of home sellers in Illinois will show that between 69% and 81% of homes are sold by a
real estate agent.
C. If you sell a home in Illinois, you have an 75% ± 6% chance of using a real estate agent.
D. We are 95% confident that between 69% and 81% of homes in this survey are sold by a real estate agent.
E. We are 95% confident, based on this sample, that the interval 69% and 81% contains the true proportion of all
homes in Illinois that are sold by a real estate agent.
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42. A process is producing material which is 20% defective. Five pieces are selected at random for inspection. What
is the probability of exactly three good pieces being found in the sample?
A. 0.184
B. 0.061
C. 0.205
D. 0.051
43. You’re executing a sampling plan where you pull 60 samples from a production lot that is known to have a
3.33% defective rate. What is the probability that you get 2 defective units in that sample?
A. 100%
B. 27.5%
C. 3.33%
D. 55.0%
44. The expression below is which of the following?
𝑛!
∙ 𝑝 𝑥 ∙ (1 − 𝑝)𝑛−𝑥
(𝑥!)(𝑛 − 𝑥)!
A. General term for the Poisson distribution
C. General term for the binomial distribution
B. General term for the normal distribution
D. General term for the chi-square distribution
III.C: Normal Approximation to the Binomial
45. For the given binomial sample size and null hypothesized value of p0, determine whether the sample size is large
enough to use the normal approximation methodology to conduct a test of the null hypothesis H 0: p = p0. The
sample size is n = 65 and the null hypothesized value is p0 = 0.8
A. Yes
B. No
C. Not enough information to determine
46-47. Suppose X is a binomial random variable with 10 trials and probability of success 0.5. That is, X ∼Bin(10, 0.5).
46. (DLE Video) Find the exact probability, P(4 ≤ X ≤ 7).
47. (DLE Video) Use the normal approximation to find P(4 ≤ X ≤ 7). Make sure to adjust the range since X is a
discrete RV.
III.C: Poisson Distribution: http://births.akselipalen.com/
48. The average number of flaws in large plate glass is 0.25 per pane. The standard deviation of this Poisson
distribution is: (Use my reference table on page Ref 1.10)
A. 0.25
B. 0.05
C. 0.75
D. 0.50
49. (DLE Video) On average, a company hires 4 people per month. In a given month, what is the probability that
exactly 7 people will be hired?
A. 0.0003
B. 0.0595
C. 0.4487
D. 0.0087
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50. (DLE Video) The Poisson distribution can be used to approximate the binomial distribution under which of the
following conditions?
A. When p is equal to or larger than 0.1 and the sample size is large
B. When p is equal to or larger than 0.1 and the sample size is small
C. When p is equal to or smaller than 0.1 and the sample size is small
D. When p is equal to or smaller than 0.1 and the sample size is large
51. The distribution that has a mean equal to the variance is the:
A. Poisson
B. Exponential
C. Weibull
D. Rayleigh
52. Your production lot has an average defect rate of 9 defects per lot. What is the probability that a lot is produced
and exactly 3 defects were observed? (Argh … the answers are percentages and NOT probabilities.)
A. 33.33%
B. 0.27%
C. 1.50%
D. Not enough information
53. (DLE Video) A sample of 50 computer chips is taken from a continuous process. The current defect rate for this
process is 5%. What is the probability of finding four defects in the sample using the Poisson distribution?
A. 39.06%
B. 13.36%
C. 76.57%
D. 2.5%
54. (DLE Video) A scoop samples 100 units/trial. What must be the average number of defects for there to be an
80% chance that more than one defect will be found in the sample?
55. Historically, the number of flaws in the finish of surface has an average of 0.45. What is the probability of a
randomly selected item having more than 1 defect in the surface finish?
A. 0.0755
B. 0.2869
C. 0.6376
D. 0.3624
III.C: Normal Distribution
56. (DLE Video) The weights of oranges in a good year are described by a normal distribution with μ = 16 and σ = 2
(ounces). What is the probability that a randomly selected orange has weight in excess of 17 ounces?
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57. Sales at the McDonald’s restaurant on Route 46 by the Interstate are normally distributed with mean $34,000
and standard deviation $1,500 during a given sales period. During the most recent sales period, sales were reported
to the local taxing authority at $25,000. Should the IRS be suspicious?
Yes
No
Not enough information to determine
58. For the normal probability distribution, the relationships among the median, mean, and mode are:
A. They are all equal to the same value
B. The mean and mode have the same value, but the median is different
C. Each has a value different from the other two
D. The mean and median are the same, but the mode is different
59. Hardness of a rubber product doesn't follow a normal distribution, but the mean and standard deviation of a
sample of size n = 36 are 𝑥̅ = 70 and s = 6 Shore A (the hardness scale). What is the 95% confidence interval for
population mean? (Note to self: Check t distribution.)
A. 68.355 < µ < 71.345
B. The population standard deviation is not known so we cannot calculate the confidence interval.
C. 68.04 < µ < 71.96
D. The distribution is not Normal so we cannot calculate the confidence interval.
60. For a normal distribution, two standard deviations on each side of the mean would include approximately what
percentage of the total population?
A. 95%
B. 68%
C. 47%
D. 34%
61. What is the fewest number of samples required to achieve a confidence level of 99% that when fed a new diet,
the average weight gain of a sheep over a 90 day period had increased by 5 pounds over the current average of 20
pounds? The weight gain per sheep is normally distributed with a standard deviation of 4.3 pounds.
A. 31
B. 101
C. 71
D. 123
62. The process drift in machining operation is said to be normally distributed with a mean of 46.23 seconds and a
standard deviation of 3 seconds. What is the probability that the drift of this operation will be less than 52.81
seconds when the next measurement is taken?
A. 0.0143
B. 0.98571
C. 0.4857
D. 1.00
63. (DLE Video) You are studying the process of producing chicken feed. You want to find out if making a change to
one of the pieces of equipment will change the daily mean output for that process by 12,000 pounds. Historically,
the standard deviation of the daily production of chicken feed is 36,000 pounds. Which option represents the
minimum sample size required to confirm the significance of a shift for the mean output that is more than 12,000
pounds at a 95% confidence level (z = 1.96), assuming a normal distribution?
A. 5
B. 21
C. 35
D. 3
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III.C: Chi-Square Distribution
64. Given the following data, what is the 90% confidence interval for the variance? 22, 23, 19, 17, 29, 25
A. [4.21, 99.07]
B. [15.32, 28.66]
C. [8.27, 79.88]
D. [16.87, 56.52]
65. The results of a designed experiment are to be analyzed using a chi-square test. There are five treatments under
consideration and each treatment falls under two categories (success or failure). The calculated value of chi-square
is compared to the tabulated chi-square with how many degrees of freedom?
A. 10
B. 9
C. 5
D. 4
66. (DLE Video, from lesson notes) A poker-dealing machine is supposed to deal cards at random, as if from an
infinite deck. In a test, you counted 1600 cards, and observed the following:
Spades 404
Hearts 420
Diamonds 400
Clubs 376
Are the suits equally likely at α = 0.05? Or are these discrepancies too much to be random?
67. Three trainees were given the same lot of 50 pieces and asked to classify them as defective or non- defective,
with the following results:
Using a level of significance of α = 0.050 to determine whether or not there is a difference in the ability of the three
trainees to properly classify the parts, which of the following statements is true?
A. The chi-square calculated value is 5.99
C. No determination can be made, more data is required
B. The critical value of the chi-square is 6.88
D. The null hypothesis is rejected
68. When making inferences about a population variance based on a single sample from that population, what
distribution is used?
A. Chi-square
B. Normal
C. t distribution
D. F distribution
69. It is desirable to reduce the variation in a process. The current variance is known to be six. A new process yielded
a standard deviation of two for twenty-five trials. What is the chi-square calculated statistic?
A. 13.85
B. 15.66
C. 16.00
D. 18.24
70. It is desirable to reduce the variation in a process. The current variance is known to be seven. A new process
yielded a standard deviation of two for twenty-five test trials. What is the calculated statistic and decision for 95%
confidence?
A. 13.71, reject the null
C. 13.85, reject the null
B. 13.71, fail to reject the null
D. 13.85, fail to reject the null
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III.C: t distribution
71. Which of the following distributions have their x-axis starting at 0?
A. Normal and t
B. Normal and chi-square
C. Chi-square and F
D. F and t
72. The critical value for t, when making a two-tailed paired t test, with a sample size of 13, and α = 0.05 is:
A. 1.782
B. 2.179
C. 2.064
D. 1.711
73. (DLE Video) In order to test whether the average output of a new machine is different than the existing machine,
a sample of ten pieces was taken from each. The calculated t-value turned out to be 1.767. Using a level of
significance of 0.10, and given that the variances are unknown, but considered equal, the conclusion is:
A. The obtained t ratio does not fall within the critical region
C. There was no significant difference between the means
B. The null hypothesis was rejected
D. The null hypothesis failed to be rejected
Important note: When comparing two means with a t test assuming the variances are unknown, but considered
equal, the degrees of freedom is n1 + n2 – 2.
74. In a t test, α is 0.05, therefore:
A. 5% of the time we will say that there is no real difference, but in reality, there is a difference
B. 5% of the time we will say that there is a real difference when there really is not a difference
C. 95% of the time we will make an incorrect inference
D. 95% of the time the null hypothesis will be correct
75. A student's t test can be used to determine whether or not differences exist in:
A. Variability
B. Confidence intervals
C. Correlation coefficients
D. Averages
76. Which table should be used to determine a confidence interval on the mean when s is unknown, and the sample
size is 10? [They also need the assumption that the data is from a normally distributed population.]
A. z
B. t
C. F
D. χ²
77. A Six Sigma Green Belt is performing a hypothesis test of two population means. Sixteen samples of method A
and sixteen samples of method B are produced. The standard deviations are unknown but thought to be the same.
How many degrees of freedom are to be used for the t test?
A. 16
B. 30
C. 31
D. 32
78. (DLE Video) You're performing a hypothesis test for the population mean and the population standard deviation
is unknown. You sample 14 units from your population, and you'd like to use a 2-sided test at a 5% significance
level. What is the rejection criterion for this hypothesis test?
A. 1.771
B. 2.160
C. 2.145
D. 1.761
79. Which option describes a paired t test interference test?
A. The difference in means is calculated from two samples with unknown, but assumed unequal, variances
B. The difference in means is calculated from two samples with unknown, but assumed equal, variances
C. The variances of two samples' data are compared for equality
D. The difference in means is calculated from data collected in tandem from two samples
80. Find the value of t0 such that the following statement is true: P(-t0 < μ < t0) = 0.95, where df = 15.
A. 2.602
B. 2.947
C. 2.131
D. 1.753
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81. (DLE Video, problem in lesson notes) Average heart rate for Americans is 72 beats/minute. A group of 25
individuals participated in an aerobics fitness program to lower their heart rate. After six months the group was
evaluated to identify is the program had significantly slowed their heart. The mean heart rate for the group was 69
beats/minute with a standard deviation of 6.5. Was the aerobics program effective in lowering heart rate?
III.C: F distribution
82. What is the practical use of the F distribution?
A. To study the equality of two means
C. To study the equality of one mean and one variance
B. To study the equality of goodness of fit data
D. To study the equality of two variances
83. (DLE Video) Determine the approximate value of P(F > 4.48) given degrees of freedom υ1 = 4 and υ2 = 10. If we
are performing a hypothesis test at level of significance α = 0.05, should we reject H0 based on the test statistic F4,10
= 4.48?
84. Determine F0.95, 3, 8.
85. One-way analysis of (ANOVA) is most similar in its objectives to:
A. A test of a population mean
C. A test for equality of two population means
B. A test for equality of two sample proportions
D. A chi-square test for independence
86. If a one-tail F test (95% confidence) with ten samples yielded a variance of nine, and nine samples yielded a
variance of four, what F critical value would be used?
A. 3.23
B. 3.44
C. 3.39
D. 3.14
87. What would be the calculated F statistic if a one-tail F test (95% confidence) with ten samples, yielding a
variance of nine, and nine samples yielding a variance of four.
A. 2.25
B. 3.39
C. 3.44
D. 5.06
III.C: Which distribution is correct?
88.(a) This distribution is used to model situations having only two possible outcomes, usually labeled as success or
failure, is the:
A. Poisson
B. Binomial
C. Normal
D. Chi-square
(b) To determine probabilities for this distribution, you need the sample size n and probability p of a successful trial.
A. Poisson
B. Binomial
C. Normal
D. Chi-square
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89.(a) This distribution is used to model the number of successes in a given time interval.
A. Poisson
B. Binomial
C. Normal
D. Chi-square
C. Normal
D. Chi-square
(b) This distribution’s mean and standard deviation are the same.
A. Poisson
B. Binomial
90.(a) This distribution is used to determine if there is a difference between actual and estimated values.
A. Poisson
B. Binomial
C. Normal
D. Chi-square
C. Normal
D. Chi-square
(b) This distribution is not symmetrical.
A. Uniform
B. t
91.(a) This is a continuous distribution used to construct a confidence interval for a population mean when the data
is normally distributed, the sample size is small, and the population standard deviation is not provided.
A. F
B. t
C. Normal
D. Chi-square
(b) This distribution measures variances in hypothesis testing (ANOVA).
A. F
B. t
C. Normal
D. Chi-square
92.(a) This is a continuous distribution used to construct a confidence interval for a population mean when the data
is normally distributed, the sample size is small, and the population standard deviation is not provided.
A. F
B. t
C. Normal
D. Chi-square
(b) This distribution has the majority of its observations centered about the average and the other observations are
equally likely to occur above or below the average.
A. F
B. Poisson
C. Normal
D. Chi-square
93.(a) Which of the following hypothesis tests can be used to determine if the variance calculated from machine #1
on Shift A is the same as the variance on machine #1 during Shift B?
A. F
B. Poisson
C. t
D. Chi-square
(b) What inference test does not require some knowledge of a test or population variation?
A. t
B. Paired t test
C. Normal
D. Chi-square
94. A statistical software program returned a p-value of 0.023 for a test of two means. If the desired level of
significance is 0.025, then the conclusion is:
A. Reject the null hypothesis, there is no statistical difference in the means
B. Reject the null hypothesis, there is a statistical difference in the means
C. Fail to reject the null hypothesis, there is no statistical difference in the means
D. Fail to reject the null hypothesis, there is a statistical difference in the means
95. (DLE Video) The hybrid option on a $25,000 car costs $3,000. A gas mileage test found the hybrid averaged 39.1
mpg and the standard model averaged 34.7 mpg with a p-value of 0.024. At a level of significance of 5%, the
difference is:
A. Not statistically significant, buy the standard car
B. Not practically significant, buy the hybrid car
C. Statistically significant, but not practically significant (I’m assuming you drive 10k miles/year and gas is $4/gallon)
D. Statistically significant, one should buy the hybrid
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96. Identify the confidence interval calculation that is most likely to be non-symmetrical:
A. Means for larger samples
C. Variation confidence interval
B. Means for small samples
D. Proportion confidence interval
97.(a) The average age of the students in a statistics class is 22 years. Does this statement describe descriptive or
inferential statistics?
A. Inferential statistics
B. Descriptive statistics
(b) From past figures, it is predicted that 30% of the registered voters will vote in the May 3rd primary. Does this
statement describe descriptive or inferential statistics?
A. Inferential statistics
B. Descriptive statistics
98. Which of the following is not an element of descriptive statistical problems?
A. Information revealed in a data set is summarized
B. Predictions are made about a larger set of data
C. Data are displayed visually in graphs
D. Patterns in a data set are identified
99. If events cannot occur simultaneously, they are called:
A. Randomly selected
B. Mutually exclusive
C. Independent
D. Statistically stable
100. In determining a process average fraction defective using inductive or inferential statistics, one would
be using:
A. Statistics, computed from samples, to make inferences about populations
B. Populations, computed from samples, to make inferences about populations
C. Samples, computed from statistics, to make inferences about populations
D. Samples, computed from populations, to make inferences about samples
III.B.2 & III.C VIDEOS
• Central Limit Theorem
• Construction of confidence interval for μ with normal distribution, careful of language
• Standard error vs margin of error
• Descriptive vs inferential stats - include pop parameters vs sample statistics
• Discrete vs. continuous random variables
• Binomial
• Normal approximation to the binomial distribution
• Poisson videos, binomial estimation
• Normal distribution
• Chi-square distribution
• t distribution
• F distribution
• Various applications of these topics on Exam 7