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Stat Final Exam Review
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Questions in this quiz (41)
1The sampling distribution of the sample mean x̄ is always given by a normal curve
- ATrue
- BFalse
2Suppose a 95% CI for μ is given by (1.38, 2.74). Then, based on the CI for μ, a valid conclusion would be μ > 0.
- ATrue
- BFalse
3The value of a parameter may change as the sample values change.
- ATrue
- BFalse
4A negative assignment of probability is valid when the subjective assignment
method is used.- ATrue
- BFalse
5The sampling distribution for X is always given by
x̄ ~ N ( μ, σ/√n) when the sampled population is
~ N (μ, σ^2) and a random sample is obtained- ATrue
- BFalse
6If the variables A and B have a positive correlation, then it is always valid to claim
A is a cause of B.- ATrue
- BFalse
7For two events A and B,
P(A U B) = P(A) + P(B) − P(A ∩ B).- ATrue
- BFalse
8An example of a statistic is a value of x̄ computed from a random sample.
- ATrue
- BFalse
9When Z ~ N (0, 1) then the relative frequency of Z > 1 equals the relative frequency of Z < −1.
- ATrue
- BFalse
10For any two disjoint events A and B, P(A ∩ B) = 0.
- ATrue
- BFalse
11Suppose a 95% CI for a population mean μ is given by (13.5, 17.32). Then there is a 5% chance that μ will fall outside this interval.
- ATrue
- BFalse
12The population mean μ is the balance point of the relative frequency histogram for the population.
- ATrue
- BFalse
13Boxplots are graphical displays of the 5-number summary
- ATrue
- BFalse
14For any event A, it is always the case that 0 ≤ P(A) ≤ 1.
- ATrue
- BFalse
15Suppose an event A can only take the values {−5,−3,−2}, then P(A < 0) = −1.
- ATrue
- BFalse
16Suppose the resting pulse rate for all runners in the 2015 New York City marathon a week after the event has a mean of μ = 70 and standard deviation of = 3. Suppose 64 runners will be randomly selected from this population.
The distribution of x̄, the sample average resting pulse rate, is given by:- Ax̄ ~ N (70, 3) by CLT
- Bx̄ ~ N (3, 70) by CLT
- Cx̄ ~ N (70, 3/8) by result (1)
- Dx̄ ~ N (70, 3/8) by CLT
17Suppose the resting pulse rate for all runners in the 2015 New York City marathon a week after the event has a mean of μ = 70 and standard deviation of = 3. Suppose 64 runners will be randomly selected from this population.
Find the probability that the sample average resting pulse rate of the 64 runners exceeds 70.9375- A0.9938
- B0.4522
- C0.5478
- D0.0062
18Consider the attached probability distribution:
Find the probability the X equals 3
- A0.3
- B0.4
- C0.35
- D0.5
19Consider the attached probability distribution:
Find the probability that X exceeds 3- A0.85
- B0.35
- C0.45
- D0.10
20Consider the attached probability distribution:
Find the probability that X does not equal 3.- A0.35
- B0.6
- C0.15
- D0.10
21The CDC wants to estimate the percentage of patients with aortic valve disease within the population of all U.S. patients diagnosed with congestive heart failure. Researchers obtain a random sample of 300 patients diagnosed with congestive heart failure and determine 12% have aortic valve disease.
The population of interest to the CDC researcher is:- AAll U.S. patients
- BAll U.S. patients diagnosed with congestive heat failure
- CAll U.s patients diagnosed with aortic valve disease
- DThe percentage of all U.S. patients diagnosed with congestive heart failure who have aortic valve disease
22The CDC wants to estimate the percentage of patients with aortic valve disease within the population of all U.S. patients diagnosed with congestive heart failure. Researchers obtain a random sample of 300 patients diagnosed with congestive heart failure and determine 12% have aortic valve disease.
The dependent variable of interest to the researcher is:- Awhether or not a patient has aortic valve disease
- Bthe percentage of all patients in the population who have aortic valve disease
- Cthe number of deaths caused by aortic valve disease
- Dwhether or not a patient is diagnosed with congestive heart failure
23The CDC wants to estimate the percentage of patients with aortic valve disease within the population of all U.S. patients diagnosed with congestive heart failure. Researchers obtain a random sample of 300 patients diagnosed with congestive heart failure and determine 12% have aortic valve disease.
What does the value 12% represent?- Aa parameter
- Ba statistic
- Ca sample
- Dan experimental unit
24The CDC wants to estimate the percentage of patients with aortic valve disease within the population of all U.S. patients diagnosed with congestive heart failure. Researchers obtain a random sample of 300 patients diagnosed with congestive heart failure and determine 12% have aortic valve disease.
An example of a research inference the CDC researchers could make would be:- ABased on the population results, we believe 12% of all congestive heart disease patients have aortic valve disease.
- B12 % of the sample has aortic valve disease
- CAortic valve disease is a cause of death
- DThe sample percentage is 12%, thus estimate the percentage in the population who have aortic valve disease is 12%.
25You have measured the systolic blood pressure of a random sample of 100 employees of a large company located near you. You use the default confidence interval formula of a statistical software package to calculate a 90% confidence interval for the mean systolic blood pressure for all employees of this company (denoted by μ). The calculated confidence interval is (122, 138).
What requirements are necessary for this confidence interval to be valid?- AThe sample mean equals the population mean
- BThe sample was randomly selected from and approximately normal population
- CThe population mean has an approximate normal distribution
- DA random sample and the sampling distribution of the sample mean given by x̄ ~ N (μ, σ/√100)
26You have measured the systolic blood pressure of a random sample of 100 employees of a large company located near you. You use the default confidence interval formula of a statistical software package to calculate a 90% confidence interval for the mean systolic blood pressure for all employees of this company (denoted by μ). The calculated confidence interval is (122, 138).
Which of the following statements gives a valid interpretation of the phrase “90% confident
μ is in the interval (122, 138)”?- A90% of the population of employees have a systolic blood pressure between 122 and 138.
- BThe method used to obtain the interval has a 90% chance of producing an interval that contains the population mean systolic blood pressure.
- CThe probability that the population mean blood pressure is between 122 and 138 is .90.
- DBoth B and C
27Which of the following statements about power is true?
- Apower = P (conclude H1 given H1 is true)
- Bpower = P (conclude H1 given Ho is true)
- Cpower = P (conclude Ho given Ho is true)
- Dnone of the above statements are true
28In the last mayoral election in a large city, 47% of the adults over the age of 65 voted
Republican. A researcher wishes to determine if the proportion of adults over the age of
65 in the city who plan to vote Republican in the next mayoral election has changed. Let
p represent the proportion of the population of all adults over the age of 65 in the city
who plan to vote Republican in the next mayoral election. In terms of p, the researcher
should test which of the following null and alternative hypotheses?- AHo: p = 0.47 vs. H1: p < 0.47
- BHo: p = 0.47 vs. H1: p ≠ 0.47
- CHo: p = 0.47 vs. H1: p > 0.47
- DNone of the above
29A random sample of size n = 36 is to be drawn from a population with μ = 500 and
σ = 200. What is the probability that the sample mean exceeds 400?- A0.6815
- BApproximately 0
- C0.3085
- D0.9987
30The variance of 10 measurements of people’s height (in inches) is computed to be 25. The
standard deviation of these measurements is- A5
- B2.5
- C0.25
- D625
31A group of Stanford University medical researchers are studying the population of all U.S. adults age 50-75 who, six months ago, had arthroscopic knee surgery in order to reduce pain caused by degenerative knee conditions. The researchers believe the mean pain score for the population will be less than 48. For this study pain is measured on a 100 point count scale. That is, the possible values for the pain score are {1, 2, . . . , 100}. The researchers will obtain a random sample of size n = 81 from the population and employ a t-test to test their hypothesis.
What is the population of interest?- AAll Stanford University medical researches
- BAll U.S. adults age 50-75 who, six months ago, had arthoscopic knee surgery in order
to reduce pain caused by degenerative knee conditions - CAll U.S adults aged 50-75
- DAll of the 81 adults in the sample
32A group of Stanford University medical researchers are studying the population of all U.S. adults age 50-75 who, six months ago, had arthroscopic knee surgery in order to reduce pain caused by degenerative knee conditions. The researchers believe the mean pain score for the population will be less than 48. For this study pain is measured on a 100 point count scale. That is, the possible values for the pain score are {1, 2, . . . , 100}. The researchers will obtain a random sample of size n = 81 from the population and employ a t-test to test their hypothesis
Define the parameter of interest to the researcher- AThe value of 48
- BThe average pain score for adults in the sample
- CThe average pain score for adults in the population
- DThe average age for adults in the population
33A group of Stanford University medical researchers are studying the population of all U.S. adults age 50-75 who, six months ago, had arthroscopic knee surgery in order to reduce pain caused by degenerative knee conditions. The researchers believe the mean pain score for the population will be less than 48. For this study pain is measured on a 100 point count scale. That is, the possible values for the pain score are {1, 2, . . . , 100}. The researchers will obtain a random sample of size n = 81 from the population and employ a t-test to test their hypothesis
State H0 and Ha of interest to the researchers.- AH0: μ > 48 Ha: μ = 48
- BH0: μ = 48 Ha: μ > 48
- CH0: μ < 48 Ha: μ = 48
- DH0: μ = 48 Ha: μ < 48
34A group of Stanford University medical researchers are studying the population of all U.S. adults age 50-75 who, six months ago, had arthroscopic knee surgery in order to reduce pain caused by degenerative knee conditions. The researchers believe the mean pain score for the population will be less than 48. For this study pain is measured on a 100 point count scale. That is, the possible values for the pain score are {1, 2, . . . , 100}. The researchers will obtain a random sample of size n = 81 from the population and employ a t-test to test their hypothesis
Give the sample statistic needed to conduct the test- Aμ = the mean pain score for the population
- Bx̄ = the mean pain score for the sample
- Cthe average age for adults in the population
- Dthe average age for adults in the sample
35A group of Stanford University medical researchers are studying the population of all U.S. adults age 50-75 who, six months ago, had arthroscopic knee surgery in order to reduce pain caused by degenerative knee conditions. The researchers believe the mean pain score for the population will be less than 48. For this study pain is measured on a 100 point count scale. That is, the possible values for the pain score are {1, 2, . . . , 100}. The researchers will obtain a random sample of size n = 81 from the population and employ a t-test to test their hypothesis
Suppose the researchers obtained a t-test statistic value of -2.37 and a p-value of 0.01. Define the p-value- Ap-value = P(t(80) > −2.37|H0 true)
- Bp-value = P(t(80) < −2.37|H0 true)
- Cp-value = P(t(81) > −2.37|H0 true)
- Dp-value = P(t(81) < −2.37|H0 true)
36A group of Stanford University medical researchers are studying the population of all U.S. adults age 50-75 who, six months ago, had arthroscopic knee surgery in order to reduce pain caused by degenerative knee conditions. The researchers believe the mean pain score for the population will be less than 48. For this study pain is measured on a 100 point count scale. That is, the possible values for the pain score are {1, 2, . . . , 100}. The researchers will obtain a random sample of size n = 81 from the population and employ a t-test to test their hypothesis
State the appropriate conclusion at significance level α = .05:.- Afail to reject H0
- Breject H0 in favor of Ha
- Cconclude μ < 48
- Dconclude μ > 0.05
37A group of Stanford University medical researchers are studying the population of all U.S. adults age 50-75 who, six months ago, had arthroscopic knee surgery in order to reduce pain caused by degenerative knee conditions. The researchers believe the mean pain score for the population will be less than 48. For this study pain is measured on a 100 point count scale. That is, the possible values for the pain score are {1, 2, . . . , 100}. The researchers will obtain a random sample of size n = 81 from the population and employ a t-test to test their hypothesis
Give the assumptions required for this test to be valid (aka have high power)- Aa random sample and the sampling distribution of the test statistic is normal
- Bhave a random sample
- Cthe sampling distribution of x̄ is normal
- Da random sample and the sampling distribution of x̄ is normal
38A random sample of size n = 49 is obtained from a population with mean μ = 3 and standard deviation σ = 1.4, and X is calculated.
Give the distribution of x̄ and justify your answer- Ax̄ ~ N (3, 1.96) by CLT
- Bx̄ ~ N (3, 1.4) by CLT
- Cx̄ ~ N (3, 1.4/√49) by result (3) of section 5.6
- Dx̄ ~ N (3, 1.4/7) by CLT
39A random sample of size n = 49 is obtained from a population with mean μ = 3 and standard deviation σ = 1.4, and X is calculated.
Find the probability a value of x̄ falls in the interval (2.65, 3.426)- A0.9834
- B0.2166
- C0.9433
- D0.0401
40A random sample of size n = 49 is obtained from a population with mean μ = 3 and standard deviation σ = 1.4, and X is calculated.
Define the relevant experiment corresponding to the probability found in the last question- AObtain a sample of size n=49 and calculate x̄
- BObtain a random sample of size n=49
- CCalculate x̄
- DObtain a random sample of size n=49 and calculate x̄
41A random sample of size n = 49 is obtained from a population with mean μ = 3 and standard deviation σ = 1.4, and X is calculated.
interpret the probability found two questions ago (#39)- AAs the experiment is repeated to infinity, the proportion of x̄ values in the interval will converge to the probability.
- BAs the experiment is repeated to infinity, the percentage of x̄ values in the interval will converge to the probability.
- CThe chance a value of x̄ falls in the interval will converge to the probability.
- DAs the experiment is repeated to infinity, replacing each sample, the proportion of x̄ values in the interval will converge to the probability.
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- Statistics Quiz on Stat Final Exam Review , created by Madison Skeel on 07/12/2021.
- Author
- Madison Skeel
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- Created on 7 Dec 2021 · updated on 7 Dec 2021
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