STATS: cumulative exam review
In a survey of 2277 adults, 718 say they believe in UFOs. Construct a 90% confidence interval for the population proportion of adults who believe in UFOs.
(0.299, 0.331) With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
Determine which numbers could not be used to represent the probability of an event.
-1.5 because probability values cannot be less than 0 64/25 because probability values cannot be more than 1
A probability experiment consists of rolling a fair 8-sided die. Find the probability of the event below. rolling a 5
0.125
What is the total area under the normal curve?
1
Choose the data set where the median and mode of the set are equal.
1, 1, 7, 7, 7, 8, 8
A data set includes the entries 3, 5, 6, 8, 8, and 11. Complete the data set with an entry between 1 and 11 so that the median and mode of the set are equal.
8
The probability that an event will happen is P(E)=20/29. Find the probability that the event will not happen.
9/29
What is a discrete probability distribution?
A discrete probability distribution lists each possible value a random variable can assume, together with its probability. Your answer is correct.
There were 100 random samples of the same size taken from a population which is known to have a normal distribution with some mean and a known standard deviation. A 95% confidence interval for the population mean was constructed for each of the 100 random samples. If all the conditions are satisfied, what percentage of these confidence intervals would capture the true population mean?
Approximately 95% of them
Quantitative
A ________________ variable counts or measures something and has numeric values
Parameter
A _________________ is a numerical measurement describing some characteristic of a population.
statistic
A _________________ is a numerical measurement describing some characteristic of a sample.
A p-value is the probability _____________.
A p-value is the probability of observing the actual result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true.
What is the difference between class limits and class boundaries?
Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them. For integer data, the corresponding class limits and class boundaries differ by 0.5.
You are applying for a job at two companies. Company A offers starting salaries with μ=$35,000 and σ=$2,000. Company B offers starting salaries with μ=$35,000 and σ=$5,000. From which company are you more likely to get an offer of $39,000 or more?
Company B, because data values that lie within one standard deviation from the mean are considered very usual.
Decide whether the random variable x is discrete or continuous. Explain your reasoning. Let x represent the time it takes to run a mile.
Continuous, because x is a random variable that cannot be counted.
Decide whether the random variable x is discrete or continuous. x represents the number of motorcycle accidents in one year in California.
Discrete
observational study
Do people walk faster in an airport when they are departing (getting on a plane) or after they have arrived (getting off a plane)? An interested passenger watched a random sample of people departing and a random sample of people arriving and measured the walking speed (in feet per minute) of each. What type of study design is being performed?
Nurses wondered if birth weights of babies are going up. They knew that the average birth weight of a baby last year was 7.6 pounds. A random sample of 15 weights of babies at the hospital where the nurses work gave an average birth weight of 7.9 pounds. Nurses felt that the birth weights this year were normally distributed. Which of the following is true about the distribution of sample means?
Even though the sample size is less than 30, the distribution of sample means will be normal because the population data follow a normal distribution.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. In a frequency distribution, the class width is the distance between the lower and upper limits of a class.
False. In a frequency distribution, the class width is the distance between the lower or upper limits of consecutive classes.
The standard deviation is zero.
If all the data values in a set are identical, what can you conclude about the standard deviation?
Describe the difference between the value of x in a binomial distribution and in a geometric distribution
In a binomial distribution, the value of x represents the number of successes in n trials, while in a geometric distribution, the value of x represents the first trial that results in a success.
experiment
In a television advertisement, a company called "Waist Away" claimed the workout program on their set of DVDs would help people lose weight more than any other DVD workout program. To test this claim, an independent company, called "Slim Down," selected one other DVD program. They then randomly assigned half the volunteers to the Waist Away program and the other half to the Slim Down program. Each participant was weighed before they started the program and then regularly participated in their assigned program for one month. After one month, each participant was weighed again. The percent of weight lost was recorded for each person, where negative values indicated a weight gain. What type of study was performed?
Which of the following would increase the width of a confidence interval for a population mean?
Increase the level of confidence
What are some benefits of using graphs of frequency distributions?
It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution.
What is an advantage of using the range as a measure of variation?
It is easy to compute.
What is a disadvantage of using the range as a measure of variation?
It uses only two entries from the data set.
What are some benefits of representing data sets using frequency distributions?
Organizing the data into a frequency distribution can make patterns within the data more evident.
Describe the relationship between quartiles and percentiles
Quartiles are special cases of percentiles. Q1 is the 25th percentile Q2 is the 50th percentile Q3 is the 75th percentile
What is the difference between relative frequency and cumulative frequency?
Relative frequency of a class is the percentage of the data that falls in that class, while cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.
correlation coefficient
The correlation coefficient is a measure that describes the direction and strength of the linear relationship between two quantitative variables.
What is the definition of mode?
The data entry that occurs with the greatest frequency.
Determine whether the graph shown could represent a variable with a normal distribution. Explain your reasoning. If the graph appears to represent a normal distribution, estimate the mean and standard deviation.
The graph could not represent a variable with a normal distribution because the graph is skewed to the left.
Nurses wondered if birth weights of babies are going up. They knew that the average birth weight of a baby last year was 7.6 pounds. A random sample of 65 weights of babies at the hospital where the nurses work gave an average birth weight of 7.9 pounds. Which of the following statements is true?
The nurses can use the sample data to make an inference about birth weights at this hospital, but should be cautious about making inferences about birth weights beyond this hospital.
What are the two conditions that determine a probability distribution?
The probability of each value of the discrete random variable is between 0 and 1, inclusive, and the sum of all the probabilities is 1
Explain how to find the range of a data set.
The range is found by subtracting the minimum data entry from the maximum data entry.
Determine whether the approximate shape of the distribution in the histogram shown is symmetric, uniform, skewed left, skewed right, or none of these. Justify your answer.
The shape of the distribution is skewed right because the bars have a tail to the right.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A sample statistic will not change from sample to sample.
The statement is false. A sample statistic can change from sample to sample.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. It is impossible to have a z-score of 0.
The statement is false. A z-score of 0 is a standardized value that is equal to the mean.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The midpoint of a class is the sum of its lower and upper limits divided by two.
The statement is true.
A student's score on an actuarial exam is in the 78th percentile. What can you conclude about the student's exam score?
The student scored higher than 78% of the students who took the actuarial exam
What is the definition of median?
The value that lies in the middle of the data when the data set is ordered.
Sample
The _________________ is/are a subset of the population that is being studied.
Population
The _________________ is/are the entire group of individuals or items being studied.
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. The probability of choosing 5 numbers from 1 to 50 that match the 5 numbers drawn by a certain lottery is 1 / 2,118,760 ≈ 0.00000047.
This is an example of classical probability, since every combination of 5 numbers has an equal chance of being drawn.
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. According to company records, the probability that a washing machine will need repairs during a ten-year period is 0.21.
This is an example of empirical probability, since the stated probability is calculated based on observations from the company records.
Classify the following statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. An analyst feels that a certain stock's probability of increasing in price over the next month is 0.69.
This is an example of subjective probability, since the stated probability is most likely based on intuition, an educated guess, or an estimate.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. As the size of a sample increases, the standard deviation of the distribution of sample means increases.
This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means decreases."
Match the plot with a possible description of the sample.
Time in minutes it takes a sample of employees to drive to work
Match the plot with a possible description of the sample.
Top speeds in MPH of a sample of sports cars
A stem-and-leaf plot allows for retrieval of the original data from the plot while the histogram does not.
What is an advantage to using a stem-and-leaf plot instead of a histogram to display data?
Every member (or sample) must have the same chance of being selected as every other member (or sample of the same size)
What must be true for a sample to be considered a simple random sample?
Describe the difference between the calculation of population standard deviation and that of sample standard deviation. Let N be the number of data entries in a population and n be the number of data entries in a sample data set.
When calculating the population standard deviation, the sum of the squared deviation is divided by N, then the square root of the result is taken. When calculating the sample standard deviation, the sum of the squared deviations is divided by n−1, then the square root of the result is taken.
more
When comparing two populations with the same variable of interest in the same unit of measure, the larger the standard deviation, the _____________ dispersion there is in the distribution.
Given a data set, how do you know whether to calculate σ or s?
When given a data set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a population, then σ is calculated. If the data are a sample, then s is calculated.
see graph
Which of the following scatterplots indicates a strong negative linear relationship between X and Y?
Rejecting the null hypothesis when the null hypothesis is true is called _____________.
a type I error
What are the two decisions that you can make from performing a hypothesis test?
fail to reject the null hypothesis reject the null hypothesis
What are the two types of hypotheses used in a hypothesis test? How are they related?
null and alternative they are compliments
The claim being assessed in a hypothesis test is called _____________.
null hypothesis
A study was performed on teacher perceptions of the behavior of elementary school children. Teachers rated the aggressive behavior of a sample of 1450 New York City public school children by responding to the statement, "This child threatens or bullies others in order to get his/her own way." Responses were measured on a scale ranging from 1 (never) to 5 (always). The summary statistics were x=2.15 and s=1.05. Researchers wanted to test H0: μx=3 versus HA: μx≠3. Which of the following tests is the most appropriate to use (assuming all conditions for inference are satisfied)?
one-sample t-test
A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. H0: o <= 5.1 Ha: o > 5.1
right tailed test
To transform a nonstandard normal distribution to the standard normal distribution you must transform each data value x into a z-score. Which of the following formulas is used to convert an x value into a z-score?
z = (x-μ)/σ
Determine whether the data set is a population or a sample. Explain your reasoning. The number of floors in each building in a city
Population, because it is a collection of the number of floors for all buildings in the city
Determine whether the data set is a population or a sample. Explain your reasoning. The number of radios in each household in a country.
Population, because it is a collection of the number of radios for all households in the country
In 1990, the mean pH level of the rain in Pierce County, Washington, was 5.03. A biologist claims that the acidity of rain has increased (which means that pH level of the rain has decreased). The biologist measured the pH level of rain on a random sample of 19 rainy days. The average pH level on those 19 days was 4.81 with a standard deviation of 0.17. Which of the following tests is the most appropriate to use to test the biologist's claim (assuming all conditions for inference are satisfied)?
one-sample t-test
Are women getting taller? A researcher claims that the average height of a woman aged 20 years or older is greater than the 1994 mean height of 63.7 inches. She obtains a random sample of 45 women aged 20 years or older and finds the sample mean to be 63.9 inches. Assume the population standard deviation is 3.5 inches. Which of the following tests is the most appropriate to use to test the researcher's claim (assuming all conditions for inference are satisfied)?
one-sample z-test
