According to a 2016 report from the Institute for College Access and Success 66% of all graduates from public colleges and universities had student loans. A public college surveyed a random sample of 400 graduates and found that 62% had student loans. a. Test the hypothesis that the percentage of graduates with student loans from this college is different from the national percentage. Use a significance level of 0.05. b. After conducting the hypothesis test, a further question one might ask is what proportion of graduates from this college have student loans? Use the sample data to find a 95% confidence interval for the proportion of graduates from the college who have student loans. How does this confidence interval support the hypothesis test conclusion?
> A die is rolled 5 times, and the number of spots for each roll is recorded. Explain why this is not a binomial experiment. Name a condition for use of the binomial model that is not met.
> A coin will be flipped four times, and the number of heads recorded. Explain why this is a binomial experiment. Check all four required conditions.
> A married couple plans to have four children, and they are wondering how many boys they should expect to have. Assume none of the children will be twins or other multiple births. Also assume the probability that a child will be a boy is 0.50. Explain why
> When, in a criminal court, a defendant is found “not guilty,” is the court saying with certainty that he or she is innocent? Explain.
> When a person stands trial for murder, the jury is instructed to assume that the defendant is innocent. Is this claim of innocence an example of a null hypothesis, or is it an example of an alternative hypothesis?
> If we reject the null hypothesis, can we claim to have proved that the null hypothesis is false? Why or why not?
> Explain the difference between sampling with replacement and sampling without replacement. Suppose you have the names of 10 students, each written on a 3-inch by 5-inch notecard, and want to select two names. Describe both procedures.
> Is it acceptable practice to look at your research results, note the direction of the difference, and then make the alternative hypothesis one-sided in order to achieve a significant difference? Explain.
> A psychologist is interested in testing whether offering students a financial incentive improves their video-game-playing skills. She collects data and performs a hypothesis test to test whether the probability of getting to the highest level of a video
> Human blood is divided into 8 possible blood types. The rarest blood type is AB negative. Only 1% of the population has this blood type. Suppose a random sample of 50 people is selected. Can we find the probability that more than 3% of the sample has AB
> While the majority of people who are color blind are male, the National Eye Institute reports that 0.5% of women of with Northern European ancestry have the common form of red-green color blindness. Suppose a random sample of 100 women with Northern Euro
> Suppose you are testing someone to see whether he or she can tell butter from margarine when it is spread on toast. You use many bite-sized pieces selected randomly, half from buttered toast and half from toast with margarine. The taster is blindfolded.
> By establishing a small value for the significance level, are we guarding against the first type of error (rejecting the null hypothesis when it is true) or guarding against the second type of error?
> In 2003 and 2017 Gallup asked Democratic voters about their views on the FBI. In 2003, 44% thought the FBI did a good or excellent job. In 2017, 69% of Democratic voters felt this way. Assume these percentages are based on samples of 1200 Democratic vote
> A Harris poll asked a sample of U.S. adults if they agreed with the statement “Artificial intelligence will widen the gap between the rich and poor in the U.S.” Of those aged 18 to 35, 69% agreed with the statement. Of those aged 36 to 50, 60% agreed wit
> A Harris poll asked Americans in 2016 and 2017 if they were happy. In 2016, 31% reported being happy and in 2017, 33% reported being happy. Assume the sample size for each poll was 1000. A 95% confidence interval for the difference in these proportions p
> The Perry Preschool Project was created in the early 1960s by David Weikart in Ypsilanti, Michigan. In this project, 123 African American children were randomly assigned to one of two groups: One group enrolled in the Perry Preschool, and one group did n
> Suppose you want to estimate the mean grade point average (GPA) of all students at your school. You set up a table in the library asking for volunteers to tell you their GPAs. Do you think you would get a representative sample? Why or why not?
> Pew Research reported that 46% of Americans surveyed in 2016 got their news from local television. A similar survey conducted in 2017 found that 37% of Americans got their news from local television. Assume the sample size for each poll was 1200. a. Cons
> Statistics student Hector Porath wanted to find out whether gender and the use of turn signals when driving were independent. He made notes when driving in his truck for several weeks. He noted the gender of each person that he observed and whether he or
> In 2017, the journal Obesity reported on trends in sugar-sweetened beverage (SSB) consumption. A random sample of youths aged 12 to 19 years old were asked to monitor all food and beverages consumed in a 24-hour period. The study was done in 2003 and rep
> A double-blind study using random assignment was done of pregnant women in Denmark. Women were given fish oil or a placebo during pregnancy. Their children were followed during the first 5 years of life to see if they developed asthma. The results are su
> Refer to Exercise 7.77 for information. This data set records results just for the boys. a. Find and compare the percentages that graduated for each group, descriptively. Does this suggest that preschool was linked with a higher graduation rate? b. Verif
> The Perry Preschool Project was created in the early 1960s by David Weikart in Ypsilanti, Michigan. In this project, 123 African American children were randomly assigned to one of two groups: One group enrolled in the Perry Preschool, and the other group
> In 2016 and 2017 Gallup asked American adults about their amount of trust they had in the judicial branch of government. In 2016, 61% expressed a fair amount or great deal of trust in the judiciary. In 2017, 68% of Americans felt this way. These percenta
> According to a 2017 Gallup poll, 572 out of 1021 randomly selected smokers polled believed they are discriminated against in public life or in employment because of their smoking. a. What percentage of the smokers polled believed they are discriminated a
> According to a 2017 Gallup Poll, 617 out of 1028 randomly selected adults living in the United States felt the laws covering the sale of firearms should be more strict. a. What is the value of pn, the sample proportion who favor stricter gun laws? b. Che
> In 2017 the Pew Research Center conducted a survey on family-leave practices and attitudes. Respondents were asked to complete this sentence: “When a family member has a serious health condition, caregiver responsibilities . . .â&
> You are receiving a large shipment of batteries and want to test their lifetimes. Explain why you would want to test a sample of batteries rather than the entire population.
> Pew Research published survey results from two random samples. Both samples were asked, “Have you listened to an audio book in the last year?” The results are shown in the table below. Find and compare the sample propo
> The researchers in a Pew study interviewed two random samples, one in 2015 and one in 2018. Both samples were asked, “Have you read a print book in the last year?” The results are shown in the table below. a. Find and
> Of 1019 U.S. adults responding to a 2017 Harris poll, 47% said they always or often read nutrition labels when grocery shopping. a. Construct a 95% confidence interval for the population proportion of U.S. adults who always or often read nutrition labels
> In a 2017 Harris poll conducted for Uber Eats, 438 of 1019 U.S. adults polled said they were “picky eaters.” a. What proportion of the respondents said they were picky eaters? b. Find a 95% confidence interval for the population proportion of U.S. adults
> A Gallup poll asked college students in 2016 and again in 2017 whether they believed the First Amendment guarantee of freedom of religion was secure or threatened in the country today. In 2016, 2089 out of 3072 students surveyed said that freedom of re
> In the 1960 presidential election, 34,226,731 people voted for Kennedy, 34,108,157 for Nixon, and 197,029 for third-party candidates. a. What percentage of voters chose Kennedy? b. Would it be appropriate to find a confidence interval for the proportion
> The Gallup poll reported that 45% of Americans have tried marijuana. This was based on a survey of 1021 Americans and had a margin of error of plus or minus 5 percentage points with a 95% level of confidence. a. State the survey results in confidence int
> According to a 2018 Rasmussen Poll, 40% of American adults were very likely to watch some of the Winter Olympic coverage on television. The survey polled 1000 American adults and had a margin of error of plus or minus 3 percentage points with a 95% level
> A 2017 survey of U.S. adults found the 64% believed that freedom of news organization to criticize political leaders is essential to maintaining a strong democracy. Assume the sample size was 500. a. How many people in the sample felt this way? b. Is the
> A 2017 survey of U.S. adults found that 74% believed that protecting the rights of those with unpopular views is a very important component of a strong democracy. Assume the sample size was 1000. a. How many people in the sample felt this way? b. Is the
> Refer to Exercise 6.11. What is the probability that the amount of new snow will be between 3 and 6 inches? Copy the graph from Exercise 6.11, shade the appropriate area, and report the numerical value of the probability. Graph from Exercise 6.11:
> A 2016 Pew Research poll found that 61% of U.S. adults believe that organic produce is better for health than conventionally grown varieties. Assume the sample size was 1000 and that the conditions for using the CLT are met. a. Find and interpret a 95% c
> A 2017 Gallup poll reported that 658 out of 1028 U.S. adults believe that marijuana should be legalized. When Gallup first polled U.S. adults about this subject in 1969, only 12% supported legalization. Assume the conditions for using the CLT are met. a.
> In a simple random sample of 1200 Americans age 20 and over, the proportion with diabetes was found to be 0.115 (or 11.5%). a. What is the standard error for the estimate of the proportion of all Americans age 20 and over with diabetes? b. Find the margi
> Toronto drivers have been going to small towns in Ontario (Canada) to take the drivers’ road test, rather than taking the test in Toronto, because the pass rate in the small towns is 90%, which is much higher than the pass rate in Toronto. Suppose that e
> Dolly the Sheep, the world’s first mammal to be cloned, was introduced to the public in 1997. In a Pew Research poll taken soon after Dolly’s debut, 63% of Americans were opposed to the cloning of animals. In a Pew Research poll taken 20 years after Doll
> In 2015 a Gallup poll reported that 52% of Americans were satisfied with the quality of the environment. In 2018, a survey of 1024 Americans found that 461 were satisfied with the quality of the environment. Does this survey provide evidence that satisfa
> Patients with gout also have an increased risk of cardiovascular disease. A 2018 double- blind study by White et al. reported in The New England Journal of Medicine, patients with cardiovascular disease and gout were randomly assigned to receive one of t
> California’s controversial “three-strikes law” requires judges to sentence anyone convicted of three felony offenses to life in prison. Supporters say that this decreases crime both because it is a st
> A Quinnipiac poll conducted on February 20, 2018, found that 824 people out of 1249 surveyed favored stricter gun control laws. A survey conducted one week later on February 28, 2018, by National Public Radio found that 754 out of 1005 people surveyed fa
> Chapman University conducts an annual Survey of American Fears. One of the objectives of this survey is to collect annual data on the fears, worries, and concerns of Americans. In 2017 the survey sampled 1207 participants. One of the survey findings was
> A true/false test has 50 questions. Suppose a passing grade is 35 or more correct answers. Test the claim that a student knows more than half of the answers and is not just guessing. Assume the student gets 35 answers correct out of 50. Use a significanc
> A polling agency wants to determine the sample size required to get a margin of error of no more than 3 percentage points (0.03). Assume the pollsters are using a 95% confidence level. How large a sample should they take? See above for the .
> Has trust in the legislative branch of government declined? A Gallup poll asked U.S. adults if they trusted the legislative branch of government in 2008 and again in 2017. The results are shown in the table. a. Find and compare the sample proportion for
> Has trust in the executive branch of government declined? A Gallup poll asked U.S. adults if they trusted the executive branch of government in 2008 and again in 2017. The results are shown in the table. a. Find and compare the sample proportion for thos
> Suppose a political consultant is hired to determine if a school bond is likely to pass in a local election. The consultant randomly samples 250 likely voters and finds that 52% of the sample supports passing the bond. Construct a 95% confidence interval
> A poll on a proposition showed that we are 99% confident that the population proportion of voters supporting it is between 52% and 62%. Find the margin of error.
> A poll on a proposition showed that we are 95% confident that the population proportion of voters supporting it is between 40% and 48%. Find the margin of error.
> Babies in the United States have a mean birth length of 20.5 inches with a standard deviation of 0.90 inch. The shape of the distribution of birth lengths is approximately Normal. a. Find the birth length at the 2.5th percentile. b. Find the birth length
> Find the sample size required for a margin of error of 3 percentage points, and then find one for a margin of error of 1.5 percentage points; for both, use a 95% confidence level. Find the ratio of the larger sample size to the smaller sample size. To re
> The distribution of the math portion of SAT scores has a mean of 500 and a standard deviation of 100, and the scores are approximately Normally distributed. a. What is the probability that one randomly selected person will have an SAT score of 550 or mor
> Using your list of outcomes in Problem 6.8: a. Find the probability of having 0, 1, or 2 girls in a family of two children and display the probability distribution in a table. b. Make a graph of the probability distribution. Outcomes of Problem 6.8:
> In 2017 the Gallup poll surveyed 1021 adults in the United States and found that 57% supported a ban on smoking in public places. a. Identify the population and the sample. b. What is the parameter of interest? What is the statistic?
> The resonant frequency of a certain series RLC circuit is 2.84 kHz, and the value of its capacitance is 6.50 μF. What is the value of the resonant frequency when the capacitance of the circuit is 9.80 μF?
> An RLC circuit is used in a radio to tune into an FM station broadcasting at f = 99.7 MHz. The resistance in the circuit is R = 12.0 Ω, and the inductance is L = 1.40 μH. What capacitance should be used?
> Consider a series RLC circuit with R = 25 Ω, L = 6.0 mH, and C = 25 μF. The circuit is connected to a 10. - V (rms), 600. - Hz AC source. (a) Is the sum of the voltage drops across R, L, and C equal to 10. V (rms)? (b) Which is greatest, the power delive
> An inductor and a resistor are connected in series. When connected to a 60. - Hz, 90. - V (rms) source, the voltage drop across the resistor is found to be 50. V (rms) and the power delivered to the circuit is 14 W. Find (a) The value of the resistance a
> A series RLC circuit has a resistance of 22.0 Ω and an impedance of 80.0 Ω. If the rms voltage applied to the circuit is 160. V, what average power is delivered to the circuit?
> An RLC circuit has resistance R = 225 Ω and inductive reactance XL = 175 Ω. (a) Calculate the circuit’s capacitive reactance XC if its power factor is cos ( = 0.707. Repeat the calculation for (b) Cos ( = 1.00 and (c) Cos ( = 1.00 x 10-2.
> An AC voltage of the form Δv = (90.0 V) sin (350t) is applied to a series RLC circuit. If R = 50.0 Ω, C = 25.0 μF, and L = 0.200 H, find the (a) Impedance of the circuit, (b) rms current in the circuit, and (c) Average power delivered to the circuit.
> A multimeter in an RL circuit records an rms current of 0.500 A and a 60.0 - Hz rms generator voltage of 104 V. A wattmeter shows that the average power delivered to the resistor is 10.0 W. Determine (a) The impedance in the circuit, (b) The resistance R
> An AC source operating at 60. Hz with a maximum voltage of 170 V is connected in series with a resistor (R = 1.2 kΩ) and a capacitor (C = 2.5 μF). (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potenti
> A 1.5 – kΩ resistor is connected to an AC voltage source with an rms voltage of 120 V. (a) What is the maximum voltage across the resistor? (b) What is the maximum current through the resistor? (c) What is the rms current through the resistor? (d) What i
> In which one of the following lists are different types of electromagnetic waves ranked in order of increasing wavelength? (a) X - rays, gamma rays, visible light, radio waves (b) Visible light, radio waves, gamma rays, x – rays (c) Gamma rays, x - rays,
> An AC source with a maximum voltage of 150. V and f = 50.0 Hz is connected between points a and d in Figure P21.29. Calculate the rms voltages between points (a) a and b, (b) b and c, (c) c and d, and (d) b and d. Figure P21.29:
> At what frequency does the inductive reactance of a 57.0 – μH inductor equal the capacitive reactance of a 57.0 - μF capacitor?
> A series AC circuit contains a resistor, an inductor of 150. mH, a capacitor of 5.00 μF, and a generator with ΔVmax = 240. V operating at 50.0 Hz. The maximum current in the circuit is 100. mA. Calculate (a) The inductive reactance, (b) The capacitive re
> A 60.0 - Ω resistor is connected in series with a 30.0 - μF capacitor and a generator having a maximum voltage of 1.20 x 102 V and operating at 60.0 Hz. Find the (a) Capacitive reactance of the circuit, (b) Impedance of the circuit, and (c) Maximum curre
> A person is working near the secondary of a transformer, as shown in Figure P21.25. The primary voltage is 120. V (rms) at 60.0 Hz. The capacitance Cs, which is the stray capacitance between the hand and the secondary winding, is 20.0 pF. Assuming the pe
> An AC source operating at 60. Hz with a maximum voltage of 170 V is connected in series with a resistor (R = 1.2 kΩ) and an inductor (L = 2.8 H). (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potentia
> A series RLC circuit has resistance R = 12.0 Ω, inductive reactance XL = 30.0 Ω, and capacitive reactance XC = 20.0 Ω. If the maximum voltage across the resistor is ΔVR = 145 V, find the maximum voltage across (a) The inductor and (b) The capacitor. (c)
> A 50.0 - Ω resistor, a 0.100 - H inductor, and a 10.0 - μF capacitor are connected in series to a 60.0 - Hz source. The rms current in the circuit is 2.75 A. Find the rms voltages across (a) The resistor, (b) The inductor, (c) The capacitor, and (d) The
> A resistor (R = 9.00 x 102 Ω), a capacitor (C = 0.250 μF), and an inductor (L = 2.50 H) are connected in series across a 2.40 x 102 - Hz AC source for which ΔVmax = 1.40 x 102 V. Calculate (a) The impedance of the circuit, (b) The maximum current deliver
> An inductor (L = 400. mH), a capacitor (C = 4.43 μF), and a resistor (R = 500. Ω) are connected in series. A 50.0 - Hz AC generator connected in series to these elements produces a maximum current of 250 mA in the circuit. (a) Calculate the required maxi
> As the bar in Figure CQ20.5 moves perpendicular to the field, is an external force required to keep it moving with constant speed? Figure CQ20.5:
> A certain light-bulb is rated at 60.0 W when operating at an rms voltage of 120. V. (a) What is the peak voltage applied across the bulb? (b) What is the resistance of the bulb? (c) Does a 100. - W bulb have greater or less resistance than a 60.0 - W bul
> A series RLC circuit has resistance R = 50.0 Ω and inductance L = 0.500 H. (a) Find the circuit’s capacitance C if the voltage source operates at a frequency of f = 60.0 Hz and the impedance is Z = R = 50.0 Ω. (b) What is the phase angle between the curr
> A sinusoidal voltage Δv = (80.0 V) sin (150t) is applied to a series RLC circuit with L = 80.0 mH, C = 125.0 μF, and R = 40.0 Ω. (a) What is the impedance of the circuit? (b) What is the maximum current in the circuit?
> Determine the maximum magnetic flux through an inductor connected to a standard outlet (ΔVrms = 120. V, f = 60.0 Hz).
> The output voltage of an AC generator is given by Δv = (1.20 x 102 V) sin (30πt). The generator is connected across a 0.500 - H inductor. Find the (a) Frequency of the generator, (b) Rms voltage across the inductor, (c) Inductive reactance, (d) Rms curre
> In a purely inductive AC circuit as shown in Figure P21.15, ΔVmax = 100. V. (a) The maximum current is 7.50 A at 50.0 Hz. Calculate the inductance L. (b) At what angular frequency ω is the maximum current 2.50 A? Figure P21.15:
> An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 47 - H inductor, determine (a) The inductive reactance and (b) The rms current through the inductor.
> An inductor has a 54.0 - Ω reactance when connected to a 60.0 - Hz source. The inductor is removed and then connected to a 50.0 - Hz source that produces a 100. - V rms voltage. What is the maximum current in the inductor?
> A generator delivers an AC voltage of the form Δv = (98.0 V) sin (80πt) to a capacitor. The maximum current in the circuit is 0.500 A. Find the (a) Rms voltage of the generator, (b) Frequency of the generator, (c) Rms current, (d) Reactance, and (e) Valu
> What maximum current is delivered by an AC source with ΔVmax = 48.0 V and f = 90.0 Hz when connected across a 3.70 - μF capacitor?
> When light (or other electromagnetic radiation) travels across a given region, (a) What is it that oscillates? (b) What is it that is transported?
> An AC generator with an output rms voltage of 36.0 V at a frequency of 60.0 Hz is connected across a 12.0 - μF capacitor. Find the (a) Capacitive reactance, (b) Rms current, and (c) Maximum current in the circuit. (d) Does the capacitor have its maximum
> (a) What is the resistance of a light-bulb that uses an average power of 75.0 W when connected to a 60.0 - Hz power source having a maximum voltage of 170. V? (b) What is the resistance of a 100. - W light-bulb?
> A conducting rectangular loop of mass M, resistance R, and dimensions w by â„“ falls from rest into a magnetic field B(, as shown in Figure P20.67. During the time interval before the top edge of the loop reaches the field, the loop appro
> An N-turn square coil with side â„“ and resistance R is pulled to the right at constant speed v in the positive x - direction in the presence of a uniform magnetic field B acting perpendicular to the coil, as shown in Figure P20.66. At t
> In Figure P20.65 the rolling axle of length 1.50 m is pushed along horizontal rails at a constant speed v = 3.00 m/s. A resistor R = 0.400 Ω is connected to the rails at points a and b, directly opposite each other. (The wheels make good elec
