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elementary statistics
Elementary Statistics Picturing The World 5th Edition Ron Larson, Betsy Farber - Solutions
If you lower the level of significance to a=0.01, does your decision change? Explain your reasoning.
Complete the hypothesis test for all adults (men and women) by performing the following steps. Use a level of significance of a = 0.05. (a) Sketch the sampling distribution. (b) Determine the critical values and add them to your sketch. (c) Determine the rejection regions and shade them in your
Given Ho: 8.5, Ha: < 8.5, and P = 0.0691. (a) Do you reject or fail to reject Ho at the 0.01 level of significance? (b) Do you reject or fail to reject Ho at the 0.05 level of significance?
Given Ho=100, Ha: 100, and P = 0.0461. (a) Do you reject or fail to reject Ho at the 0.01 level of significance? (b) Do you reject or fail to reject Ho at the 0.05 level of significance?
In hypothesis testing, does choosing between the critical value method or the P-value method affect your conclusion? Explain.
Explain the difference between the z-test for using rejection region(s) and the z-test for using a P-value.
If you want to support a claim, write it as your null hypothesis.
A large P-value in a test will favor rejection of the null hypothesis.
The level of significance is the maximum probability you allow for rejecting a null hypothesis when it is actually true.
If you decide to reject the null hypothesis, you can support the alternative hypothesis.
A statistical hypothesis is a statement about a sample.
In a hypothesis test, you assume the alternative hypothesis is true.
Does failing to reject the null hypothesis mean that the null hypothesis is true? Explain. True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
Describe the two types of error possible in a hypothesis test decision.
What are the two types of hypotheses used in a hypothesis test? How are they related?
Is it probable that the population proportion who most admire Sarah Palin is 18% or greater? Explain your reasoning.
Use a technology tool to simulate a most admired poll. Assume that the actual population proportion who most admire Sarah Palin is 18%. Run the simulation several times using n = 1025. (a) What was the least value you obtained for p? (b) What was the greatest value you obtained for p? MINITAB
The second most named woman was Sarah Palin, who was named by 15% of the people in the sample. Use a technology tool to find a 95% confidence interval for the population propor- tion that would have chosen Sarah Palin.
Do the confidence intervals you obtained in Exercises 1 and 2 agree with the statement issued by the Gallup Organization that the margin of error is 4%? Explain.
In 2009, the most named woman was Hillary Clinton at 16%. Use a technology tool to find a 95% confidence interval for the population. proportion that would have chosen Hillary Clinton.
In 2009, the most named man was Barack Obama at 30%. Use a technology tool to find a 95% confidence interval for the population proportion that would have chosen Barack Obama.
A trainer wants to estimate the population mean running times for both male and female runners within 2 minutes. Determine the minimum sample size required to construct a 99% confidence interval for the population mean training time of (a) male runners. Assume the population standard deviation is
5. Use the sample to construct a 95% confidence interval for the population mean training time of all runners. How do your results differ from those in Exercise 3? Explain.
Interpret the results of Exercise
Use the sample to construct a 95% confidence interval for the population mean training time of the (a) male runners. (b) female runners.
Find the standard deviation of the training times for the (a) male runners. (b) female runners.
Use the sample to find a point estimate for the mean training time of the (a) male runners. (b) female runners.
A batch of 350 raffle tickets contains four winning tickets. You buy four tickets. What is the probability that you have (a) no winning tickets? (b) all of the winning tickets? (c) at least one winning ticket? (d) at least one nonwinning ticket?
A batch of 200 calculators contains 3 defective units. What is the probability that a sample of three calculators will have (a) no defective calculators? (b) all defective calculators? (c) at least one defective calculator? (d) at least one nondefective calculator?
A security code consists of three letters followed by one digit. The first letter cannot be an A, B, or C. What is the probability of guessing the security code in one trial?
A full house consists of a three of one kind and two of another kind. Find the probability of a full house consisting of three kings and two queens.
An employer must hire 2 people from a list of 13 applicants. In how many ways can the employer choose to hire the 2 people? In Exercises 51–55, use counting principles to find the probability. Then tell whether the event can be considered unusual.
A literary magazine editor must choose 4 short stories for this month’s issue from 17 submissions. In how many ways can the editor choose this month’s stories?
Five players on a basketball team must each choose a player on the opposing team to defend. In how many ways can they choose their defensive assignments?
Fifteen cyclists enter a race. In how many ways can they finish first, second, and third?
Use a technology tool to find
42.
Find the probability of randomly selecting an adult from the sample who does not prefer a science fiction movie or an action movie. SECTION 3.4 In Exercises 41–44, perform the indicated calculation.
Find the probability of randomly selecting an adult from the sample who does not prefer a comedy.
Find the probability of randomly selecting an adult from the sample who prefers a drama or a musical.
Find the probability of randomly selecting an adult from the sample who prefers an action movie or a horror movie.
Find the probability of randomly selecting a school with between 300 and 999 students, inclusive. In Exercises 37–40, use the Pareto chart, which shows the results of a survey in which 874 adults were asked which genre of movie they preferred. (Adapted from Rasmussen Reports)
Find the probability of randomly selecting a school with 600 or more students.
In Exercises 35 and 36, use the pie chart, which shows the percent distribution of the number of students in traditional U.S. elementary schools. (Source: U.S. National Center for Education Statistics)
34. An 8-sided die, numbered 1 to 8, is rolled. Find the probability that the roll results in an even number or a number greater than
A 12-sided die, numbered 1 to 12, is rolled. Find the probability that the roll results in an odd number or a number less than
A card is randomly selected from a standard deck. Find the probability that the card is red or a queen.
A card is randomly selected from a standard deck. Find the probability that the card is between 4 and 8, inclusive, or is a club.
A sample of automobile dealerships found that 19% of automobiles sold are silver, 22% of automobiles sold are sport utility vehicles (SUVs), and 16% of automobiles sold are silver SUVs. What is the probability that a randomly chosen sold automobile from this sample is silver or an SUV? In Exercises
A random sample of 250 working adults found that 37% access the Internet at work, 44% access the Internet at home, and 21% access the Internet at both work and home. What is the probability that a person in this sample selected at random accesses the Internet at home or at work?
You are given that and Do you have enough information to find or Explain.
Event A: Randomly select a U.S. adult registered to vote in Illinois. Event B: Randomly select a U.S. adult registered to vote in Florida.
Event A: Randomly select a person who loves cats. Event B: Randomly select a person who owns a dog.
Event A: Randomly select a red jelly bean from a jar. Event B: Randomly select a yellow jelly bean from the same jar.
Your sock drawer has 18 folded pairs of socks, with 8 pairs of white, 6 pairs of black, and 4 pairs of blue. What is the probability, without looking in the drawer, that you will first select and remove a black pair, then select either a blue or a white pair? Is this an unusual event? Explain.
You are shopping, and your roommate has asked you to pick up toothpaste and dental rinse. However, your roommate did not tell you which brands to get. The store has eight brands of toothpaste and five brands of dental rinse. What is the probability that you will purchase the correct brands of both
You are given that and Do you have enough information to find and Explain. In Exercises 23 and 24, find the probability of the sequence of events.
Getting high grades and being awarded an academic scholarship
Taking a driver’s education course and passing the driver’s license exam
Tossing a coin four times, getting four heads, and tossing it a fifth time and getting a head
Find the probability that a student is a graduate student, given that the student received a minus grade. In Exercises 19–21, decide whether the events are independent or dependent. Explain your reasoning.
Find the probability that a student is an undergraduate student, given that the student received a plus grade.
What is the probability of not randomly generating your cousin’s telephone number? For Exercises 17 and 18, the two statements below summarize the results of a study on the use of plus/minus grading at North Carolina State University. It shows the percents of graduate and undergraduate students
What is the probability of randomly generating your cousin’s telephone number?
Your cousin lives within the given area code.
The next seven digits represent the local telephone numbers for that region. A local telephone number cannot begin with a 0 or
What is the probability that a randomly selected firm will have fewer than 20 employees? Telephone Numbers The telephone numbers for a region of a state have an area code of
What is the probability that a randomly selected firm will have at least 10 employees?
The chance that a randomly selected person in the United States is between 15 and 29 years old is about 21%. (Source: U.S. Census Bureau) In Exercises 13 and 14, the table shows the approximate distribution of the sizes of firms for a recent year. Use the table to determine the probability of the
The probability of rolling 2 six-sided dice and getting a sum greater than 9 is
The probability that a person can roll his or her tongue is 70%.
The chance that Corporation A’s stock price will fall today is 75%.
The probability of randomly selecting five cards of the same suit from a standard deck is about 0.0005.
On the basis of prior counts, a quality control officer says there is a 0.05 probability that a randomly chosen part is defective.
The state of Virginia’s license plates have three letters followed by four digits. Assuming that any letter or digit can be used, how many different license plates are possible? In Exercises 7–12, classify the statement as an example of classical probability, empirical probability, or
A student must choose from 7 classes to take at 8:00 A.M., 4 classes to take at 9:00 A.M., and 3 classes to take at 10:00 A.M. How many ways can the student arrange the schedule?
Experiment: Guessing the gender(s) of the three children in a family Event: The family has two boys In Exercises 5 and 6, use the Fundamental Counting Principle.
Experiment: Choosing a month of the year Event: Choosing a month that begins with the letter J
Experiment: Rolling 2 six-sided dice Event: Getting a sum of 4 or 5
In Exercises 1–4, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram if it is appropriate.Experiment: Tossing four coins Event: Getting three heads
Use a technology tool to find the standard deviation of the set of 36 sample means. How does it compare with the standard deviation of the ages?
Use a technology tool to find the standard deviation of the ages of people in the United States.
Sketch a relative frequency histogram for the 36 sample means. Use nine classes. Is the histogram approximately bell-shaped and symmetric? Does this agree with the result predicted by the Central Limit Theorem?
Are the ages of people in the United States normally distributed? Explain your reasoning.
Enter the set of sample means into a technolo- gy tool. Find the mean of the set of sample means. How does it compare with the mean age in the United States? Does this agree with the result predicted by the Central Limit Theorem?
Enter the age distribution of the United States into a technology tool. Use the tool to find the mean age in the United States.
Find the probability that at most 20 adults say they are concerned about the amount and security of personal online data that can be accessed by cybercriminals and hackers. Interpret the result.
Decide whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why.
Are you more likely to randomly select one student with an IQ score greater than 105 or are you more likely to randomly select a sample of 15 students with a mean IQ score greater than 105? Explain. In Exercises 11 and 12, use the following information. In a survey of adults under age 65, 81% say
A random sample of 60 students is drawn from this population. What is the probability that the mean IQ score is greater than 105? Interpret your result.
What is the highest score that would still place a student in the bottom 10% of the scores?
What is the lowest score that would still place a student in the top 5% of the scores?
If 2000 students are randomly selected, how many would be expected to have an IQ score that is less than 90?
What percent of the students had an IQ score that is greater than 112?
Find the probability that a student had a score between 95 and105.Is this an unusual event? Explain.
Find the probability that a student had a score higher than125.Is this an unusual event? Explain.
Find each normal probability for the given parameters. (a) = 5.5, = 0.08, P(5.36 < x < 5.64) (b) = -8.2, = 7.84, P(-5.00 < x < 0) (c) = 18.5, = 9.25, P(x < 0 or x > 37) In Exercises 3-10, use the following information. Students taking a standardized IQ test had a mean score of 100 with a standard
Find each standard normal probability. (a) P(z > -2.54) (b) P(z < 3.09) (c) P(-0.88 -0.715)
A birth weight of less than 3.25 pounds is classified by the NCHS as a "very low birth weight." What is the probability that a baby has a very low birth weight for each gestation period? (a) Under 28 weeks (c) 32 to 33 weeks (b) 28 to 31 weeks (d) 37 to 39 weeks
For each gestation period, what is the proba- bility that a baby will weigh between 6 and 9 pounds at birth? (a) Under 28 weeks (b) 28 to 31 weeks (c) 34 to 36 weeks (d) 37 to 39 weeks
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