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mathematics
fundamentals of statistics
Questions and Answers of
Fundamentals of Statistics
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two tailed. What parameter is being tested?H0: p = 0.2H1: p < 0.2
The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two tailed. What parameter is being tested?H0: μ = 5H1: μ > 5
True or False: Sample evidence can prove a null hypothesis is true.
The _______ is the probability of making a Type I error.
According to the Pew Research Center, the proportion of the American population who use only a cellular telephone (no landline) is 0.37. Jason conducts a survey of thirty 20- to 24-year-olds who live
If we do not reject the null hypothesis when the statement in the alternative hypothesis is true, we have made a Type ______ error.
If we reject the null hypothesis when the statement in the null hypothesis is true, we have made a Type ______ error.
The ______ is a statement we are trying to find evidence to support.
The _________ is a statement of no change, no effect, or no difference.
True or False: When testing a hypothesis using the P-value Approach, if the P-value is large, we reject the null hypothesis.
True or False: When testing a hypothesis using the Classical Approach, if the sample proportion is too many standard deviations from the proportion stated in the null hypothesis, we reject the null
A ________ is a statement regarding a characteristic of one or more populations.
When ________ observed results are unlikely under the assumption that the null hypothesis is true, we say the result is and we reject the null hypothesis.
The 114th Congress of the United States of America has 535 members, of which 108 are women. An alien lands near the U.S. Capitol and treats members of Congress as a random sample of the human race.
The procedure for constructing a t-interval is robust. Explain what this means.
What type of variable is required to construct a confidence interval for a population proportion?
According to Nielsen/NetRatings, the mean amount of time spent on MySpace.com per user per month in July 2014 was 171.0 minutes. A 95% confidence interval for the mean amount of time spent on
Does chewing your food for a longer period of time reduce one’s caloric intake of food at dinner? A researcher requires a sample of 75 healthy males to chew their food twice as long as they
A researcher wanted to know whether consumption of green tea on a daily basis reduces LDL (bad) cholesterol. She obtains a random sample of 500 subjects. Each subject consumes at least 1 cup of green
Researchers at the Gallup Organization asked a random sample 1016 adult Americans aged 21 years or older, “Right now, do you think the state of moral values in the country as a whole is getting
Indicate whether a confidence interval for a proportion or mean should be constructed to estimate the variable of interest. Justify your response.A developmental mathematics instructor wishes to
The area under the t-distribution with 18 degrees of freedom to the right of t = 1.56 is 0.0681. What is the area under the t-distribution with 18 degrees of freedom to the left of t = -1.56? Why?
If H0: β1 = 0 is not rejected, what is the best estimate for the value of the response variable for any value of the explanatory variable?
State the requirements to perform inference on a simple least-squares regression line.
A researcher believes that as age increases, the grip strength (pounds per square inch, psi) of an individuals dominant hand decreases. From a random sample of 17 females, he obtains the
For what type of variable does it makes sense to construct a confidence interval about a population mean?
For what type of variable does it make sense to construct a confidence interval about a population proportion?
Without doing any computation, decide which has a higher probability, assuming each sample is from a population that is normally distributed with μ = 100 and σ = 15. Explain your reasoning.(a) P(90
Explain what a sampling distribution is.
Consider the homeowners association presented at the beginning of this section. A random sample of 20 households resulted in 15 indicating that they would favor an increase in assessments. Explain
Describe the sampling distribution of p̂. Assume that the size of the population is 25,000 for each problem.n = 1010, p = 0.84
Describe the sampling distribution of p̂. Assume that the size of the population is 25,000 for each problem.n = 1000, p = 0.103
Describe the circumstances under which the shape of the sampling distribution of p̂ is approximately normal.
The standard deviation of the sampling distribution of x̅, σx̅, is called the ________ of the__________.
The ______ ______, denoted p̂, is given by the formula p̂ = ______ , where x is the number of individuals with a specified characteristic in a sample of n individuals.
Suppose a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ.The sampling distribution of x̅ has mean μx̅ = and standard deviation σx̅
In your own words, explain what a sampling distribution is.
In a town of 500 households, 220 have a dog. The population proportion of dog owners in this town (expressed as a decimal) is p = ______ .
The ___________ of the sample mean, x̅, is the probability distribution of all possible values of the random variable x̅ computed from a sample of size n from a population with mean μ and standard
Give three interpretations for the area under a normal curve.
Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.The relative frequency histogram represents the incubation times of a random
Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.The relative frequency histogram represents the length of phone calls on my
Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.The relative frequency histogram represents the waiting times (in minutes) to
Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.The relative frequency histogram represents the birth weights (in grams) of
Jane obtained a random sample of 15 college students and asked how many hours they studied last week. Is it reasonable to believe that hours studied is normally distributed? The normal probability
Find the value of z0.20.
Find the value of z0.04.
True or False: A normal score is the expected z-score of a data value, assuming the distribution of the random variable is normal.
Use the figure to answer the questions that follow.(a) What is μ?(b) What is Ï?(c) Suppose that the area under the normal curve to the right of x = 75 is 0.0668. Provide two
A random variable Z that is normally distributed with mean μ = 0 and standard deviation σ = 1 is said to have the ________.
A _________ is a graph that plots observed data versus normal scores.
Explain what “success” means in a binomial probability experiment.
(a) Construct a binomial probability distribution with the given parameters;(b) Compute the mean and standard deviation of the random variable using the methods of Section 6.1;(c) Compute the mean
Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.A baseball player who reaches base
Determine whether the distribution is a discrete probability distribution. If not, state why.x P(x)100
Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.A basketball player who makes 80% of
Determine whether the distribution is a discrete probability distribution. If not, state why.x
Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.Three cards are selected from a
Determine whether the distribution is a discrete probability distribution. If not, state why.x
State the condition required to use the Empirical Rule to check for unusual observations in a binomial experiment.
Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.A random sample of 30 cars in a used
List all the combinations of five objects a, b, c, d, and e taken two at a time. What is 5C2?
Find the value of each combination.30C4
Find the value of each combination.48C3
Find the value of each combination.40C40
Find the value of each combination.52C1
Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.A random sample of 15 college seniors
According to a study conducted by CESI Debt Solutions, 80% of married people hide purchases from their mates. In a random sample of 20 married people, find and interpret:(a) The probability exactly
What are the two requirements for a discrete probability distribution?
In computing classical probabilities, all outcomes must be equally likely. Explain what this means.
A certain digital music player randomly plays each of 10 songs. Once a song is played, it is not repeated until all the songs have been played. In how many different ways can the player play the 10
Suppose a mother already has three girls from three separate pregnancies. Does the fact that the mother already has three girls affect the likelihood of having a fourth girl? Explain.
If the 2015 Hyundai Genesis has 2 engine types, 2 vehicle styles, 3 option packages, 8 exterior color choices, and 2 interior color choices, how many different Genesis’s are possible?
List all the combinations of four objects a, b, c, and d taken two at a time. What is 4C2?
Todd is putting together an exercise routine and feels that the sequence of exercises can affect his overall performance. He has 12 exercises to select from, but only has enough time to do 9. How
An essay test in European History has 12 questions. Students are required to answer 8 of the 12 questions. How many different sets of questions could be answered?
List all the permutations of four objects a, b, c, and d taken two at a time without repetition. What is 4P2?
Explain what is meant by a subjective probability. List some examples of subjective probabilities.
List all the permutations of five objects a, b, c, d, and e taken two at a time without repetition. What is 5P2?
According to the American Veterinary Medical Association, the proportion of households owning a dog is 0.372. What is the probability that a randomly selected household owns a dog?
Find the value of each combination.12C3
According to the U.S. Department of Education, 42.8% of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care?
Find the value of each combination.10C2
If P(F) = 0.30, P(E or F) = 0.65, and P(E and F) = 0.15, find P(E).
Find the value of each combination.9C2
If P(E) = 0.60, P(E or F) = 0.85, and P(E and F) = 0.05, find P(F).
Find the value of each permutation.4P0
The sample space be S = {Chris, Adam, Elaine, Brian, Jason}. Suppose that the outcomes are equally likely.Suppose that E = {Adam}. Compute the probability of Ec.
True or False: Probability is a measure of the likelihood of a random phenomenon or chance behavior.
Suppose that you roll a pair of dice 1000 times and get seven 350 times. Based on these results, what is the probability that the next roll results in seven?
If two events E and F are independent, P(E and F) = _____ .
Suppose that E and F are two events and that N(E and F) = 420 and N(E) = 740. What is P(F/E)?
In probability, a(n) _________ is any process that can be repeated in which the results are uncertain.
Suppose events E and F are disjoint. What is P(E and F)?
Suppose that E and F are two events and that N(E and F) = 380 and N(E) = 925. What is P(F/E)?
A(n) ________ is any collection of outcomes from a probability experiment.
Suppose that events E and F are independent. In addition, P(E) = 0.45 and P(F) = 0.2. What is P(E and F)?
Suppose that P(E) = 0.8, P(F) = 0.5, and P(E and F) = 0.24. Are events E and F independent? Why?
According to Gallup, 26% of adult Americans believe their diet is very healthy.(a) What is the probability that a randomly selected adult American believes his or her diet is very healthy? Interpret
Suppose that P(E) = 0.59 and P(F/E) = 0.45. What is P(E and F)?
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