Significance Tests (μ)
Significance Tests (p)
Difference of Means & Proportions
AP Review
Space
100
In a sampling distribution with a mean of zero, what's the associated p value for (P > 2.04)?
a) 0.0207
b) 0.0414
c) 0.9793
d) 0.9586
e) 0.5
a) 0.0207
100
Which of the following will increase the power of a test?
a) Increase n.
b) Increase a (confidence level)
c) Reduce the amount of variability in the sample.
d) Consider an alternative hypothesis further from the null
e) All of the above
e) All of the above
100
Are Toyota or Nissan owners more satisfied with their vehicles? Let’s design a study to find out. We’ll select a random sample of 400 Toyota owners and a separate random sample of 400 Nissan owners. Then we’ll ask each individual in the sample: “Would you say that you are generally satisfied with your (Toyota/Nissan) vehicle?” In this problem, what are you comparing?
a) means
b) proportions
c) rates
d) random variables
b) proportions
100
In which of the following situations would it be most difficult to use a census?
a) To determine what proportion of licensed bicycles on a university campus have lights
b) To determine what proportion of students in a high school support wearing uniforms
c) To determine what proportion of registered students enrolled in a college are employed more than 20 hours each week
d) To determine what proportion of single-family dwellings in a small town have two-car garages
e) To determine what proportion of fish in Lake Michigan are bass
e) To determine what proportion of fish in Lake Michigan are bass
100
The sixth planet from the sun.
What is Saturn?
200
Which of the following is a condition for choosing a t-interval rather than a z-interval when constructing a confidence interval for the mean of a population?
a) The standard deviation of the population is unknown.
b) There is an outlier in the sample data.
c) The sample may not have been a simple random sample.
d) The population is not normally distributed.
e) The data are linked so a matched-pairs test is necessary
a) The standard deviation of the population is unknown.
200
What’s the critical z* value for an 85% confidence interval?
a) .8023
b) 1.44
c) 1.04
d) 1.96
e) 1.645
b) 1.44
200
A sample survey interviews SRSs of 500 female college students and 550 male college students. Researchers want to determine whether there is a difference in the proportion of male and female college students who worked for pay last summer. In all, 410 of the females and 484 of the males say they worked for pay last summer.
Let pM and pF be the proportions of all college males and females who worked last summer. The hypotheses to be tested are:
a) 
.
b) 
.
c) 
d) 
.
e) 
.
a) ..
200
A television news editor would like to know how local registered voters would respond to the question, "Are you in favor of the school bond measure that will be voted on in an upcoming special election?" A television survey is conducted during a break in the evening news by listing two telephone numbers side by side on the screen, one for viewers to call if they approve of the bond measure, and the other to call if they disapprove. This survey method could produce biased results for a number of reasons. Which one of the following is the most obvious reason?
a) It uses a stratified sample rather than a simple random sample.
b) People who feel strongly about the issue are more likely to respond.
c) Viewers should be told about the issues before the survey is conducted.
d) Some registered voters who call might not vote in the election.
e) The wording of the question is biased.
b) People who feel strongly about the issue are more likely to respond.
200
The term given to a large interstellar cloud of dust. Many of these colorful phenomena have been made famous by the Hubble Telescope.
What is a nebula?
300
You want to compute a 95% confidence interval for the mean of a population with an unknown population standard deviation. The sample size is 25. The value of t* you would use for this interval is:
a) 1.711
b) 2.060
c) 2.064
d) 1.708
e) 1.316
c) 2.064
300
You conduct a hypothesis test and find a p-value of 0.025. Which of the following is true?
a) You can reject H0 at a=0.01
b) You can reject H0 at a=0.05
c) You can accept H0 at a=0.05
d) You can say the probability that H0 is true at p=0.025
b) You can reject H0 at a=0.05
300
The Centers for Disease Control report a survey of randomly chosen Americans age 45 and older, which found that 51 of 100 men and 80 of 782 women suffered from some form of arthritis. You want to estimate the difference in the proportions of men and women over 45 who have arthritis with a 95% confidence interval. What standard error will you use?
a) 0.0192
b) 0.0378
c) 0.0511
d) 0.1485
e) 1.96
b) 0.0378
300
A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman, sophomore, junior, and senior classes to complete the survey. This plan is an example of which type of sampling?
a) Cluster
b) Convenience
c) Simple random
d) Stratified random
e) Systematic
d) Stratified random
300
In this process, the nuclei of atoms fuse together to form a larger nucleus.
What is nuclear fusion?
400
Compute the p-value for a random sample with n=23, s=2.33, x_bar=15.5 for the test H0: μ=14.75 vs. Ha: μ =/= 14.75. Also give a conclusion for a=0.05.
a) 0.069, reject H0
b) 1.54, don't reject H0
c) 0.069, don't reject H0
d) 0.137, don't reject H0
e) 0.137, reject H0
d) 0.137, don't reject H0
400
In a test of H0: p=0.4 against Ha: p≠0.4, a random sample of size 100 yields a standardized test statistic of z=1.28. Which of the following is closest to the P-value for this test?
a) 0.90
b) 0.40
c) 0.05
d) 0.20
e) 0.10
d) 0.20
400
A study of road rage asked random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each person was assigned a road rage score on a scale of 0 to 20. The participants were chosen by random digit dialing of phone numbers. The researchers performed a test of the following hypotheses: H0:μM=μF versus Ha:μM≠μF.
Which of the following describes a Type II error in the context of this study?
a) Finding convincing evidence that the true means are different for males and females, when in reality the true means are the same
b) Finding convincing evidence that the true means are different for males and females, when in reality the true means are different
c) Not finding convincing evidence that the true means are different for males and females, when in reality the true means are the same
d) Not finding convincing evidence that the true means are different for males and females, when in reality the true means are different
e) Not finding convincing evidence that the true means are different for males and females, when in reality there is convincing evidence that the true means are different
d) Not finding convincing evidence that the true means are different for males and females, when in reality the true means are different
400
The distribution of the diameters of a particular variety of oranges is approximately normal with a standard deviation of 0.3 inch. How does the diameter of an orange at the 67th percentile compare with the mean diameter?
a) 0.202 inch below the mean
b) 0.132 inch below the mean
c) 0.132 inch above the mean
d) 0.202 inch above the mean
e) 0.440 inch above the mean
c) 0.132 inch above the mean
400
Descending onto Mars on February 18, 2021, this rover is currently studying whether past life ever existed on our celestial neighbor.
What is Perseverance?
500
A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company must sell it to more than 20% of their customers. The company will survey a random sample of 60 customers about this issue.
State what a Type I error and a Type II error would be in context with this problem. Which one is more serious?
A Type I error would be finding convincing evidence that more than 20% of customers would pay for the upgrade, when in reality they would not. A Type II error would be not finding convincing evidence that more than 20% of customers would pay for the upgrade, when in reality more than 20% would. For the company, a Type I error is worse because they would go ahead with the upgrade and lose money.
500
The US Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal. Of these, 89 say “yes”. Construct a 99% confidence interval to estimate the proportion of all visitors who support the restrictions.
(0.489, 0.697)
500
The proportion of drivers who use seat belts depends on things like age (young people are more likely to go unbelted) and gender (women are more likely to use belts). It also depends on local law. In New York City, police can stop a driver who is not belted. In Boston at the time of the study, police could cite a driver for not wearing a seatbelt only if the driver had been stopped for some other violation. A random sample of 220 young female drivers in New York City found that 183 wear seat belts while driving. A random sample of 117 young female drivers in Boston found that 68 wear seat belts while driving.
Construct and interpret a 95% confidence interval for the difference in the proportions of young females in the two cities who wear seat belts.
(0.15, 0.35)
500
The lengths of individual shellfish in a population of 10,000 shellfish are approximately normally distributed with mean 10 centimeters and standard deviation 0.2 centimeter. Which of the following is the shortest interval that contains approximately 4,000 shellfish lengths?
a) 0 cm to 9.949 cm
b) 9.744 cm to 10 cm
c) 9.744 cm to 10.256 cm
d) 9.895 cm to 10.105 cm
e) 9.9280 cm to 10.080 cm
d) 9.895 cm to 10.105 cm
500
The term for the condition when three celestial bodies are arranged in a straight line.
What is Syzygy?