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A system has two components that operate in parallel, as shown in the following diagram. Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probabilities of failures for the components 1 and 2 during one period of operation are 0.20 and 0.03, respectively. Let F1 denote the event that component 1 fails during one period of operation, and F2 denote the event that component 2 fails during one period of operation. The component failures are independent. The event corresponding to the above system failing during one period of operation is:

F1 and F2

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 110 and standard deviation σ = 20. You suspect that incoming freshman have a mean μ, which is different from 110 because they are often excited yet anxious about entering college. To verify your suspicion, you test the hypotheses H0: μ = 110, Ha: μ 110 You give the SSHA to 50 students who are incoming freshman and find their mean score. Suppose you observed the same sample mean = 115.35, but based on a sample of 100 students. What would the corresponding P-value be?

0.0074

A group of freshmen at a local university consider joining the equestrian team. Students choose Western riding with probability P = .35, dressage with probability P = 0.45, and jumping with probability P = 0.40. The probability that a student chooses both dressage and jumping is P = 0.15, while the probability of a student choosing Western and dressage is P = 0.10. No one chooses Western and jumping. There are no horses suitable for both and each student is assigned to one horse. If two students decide to join the team, what is the probability that both are Western and dressage riders if they independently decide?

0.01

In a large population of college-educated adults, the mean IQ is 112 with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign. The probability that the sample mean IQ is greater than 115 is:

0.019.

A roulette wheel has 38 slots in which the ball can land. Two of the slots are green, 18 are red, and 18 are black. The ball is equally likely to land in any slot. The roulette wheel is going to be spun twice and the outcomes of the two spins are independent. The probability that it lands on black the first time and green the second time is:

0.0249.

A veterinary researcher takes an SRS of 60 horses presenting with colic. The average age of the 60 horses with colic is 12 years. The average age of horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of horses coming to the veterinary clinic is 8 years. The probability that a sample mean is 12 or larger for a sample from the horse population is:

0.0264.

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 110 and standard deviation σ = 20. You suspect that incoming freshman have a mean μ, which is different from 110 because they are often excited yet anxious about entering college. To verify your suspicion, you test the hypotheses H0: μ = 110, Ha: μ 110 You give the SSHA to 50 students who are incoming freshman and find their mean score. If you observe a sample mean of = 115.35, what is the corresponding P-value?

0.058

The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. What is the standard deviation of the sampling distribution of the mean?

0.0633 ounces

Twenty percent of American households own three or more cars. A random sample of 144 American households is selected. Let X be the number of households selected that own three or more cars. Using the Normal approximation, the probability that at least 34 of the households selected own at least three or more cars is:

0.140.

You randomly select 500 students and observe that 85 of them smoke. Estimate the probability that a randomly selected student smokes.

0.17.

A statistician wishing to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The average score of the 20 students on the exam was 78% and the standard deviation in the population is known to be σ = 15%. The P-value for the hypothesis H0: μ = 75 vs. Ha: μ > 75 is:

0.186.

The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age of these residents is to be computed. The probability that the average age, of the 100 residents selected is less than 68.5 years is:

0.195.

A randomly selected sample of 100 horse owners found that 72 of them feed two flakes of grass hay in the morning and one flake of alfalfa plus one flake of grass hay in the evening to their horses while the rest feed two flakes of grass hay in the morning and one flake of alfalfa plus oat hay in the evening. The estimated probability that horse owners feed grass hay in the A.M. and alfalfa plus oat hay in the P.M. is:

0.28.

If X has a binomial distribution with 20 trials and a mean of six, then the success probability p is:

0.30.

Students at a local university have the option of taking freshman seminars during their first year in college. A survey of the freshmen revealed the following: Among the social science majors, 50% chose to take a freshman seminar; among the humanities majors, 65% chose to take a freshman seminar; and among the physical science majors, it was 30%. Among the freshmen 50% are social science majors, 35% are humanities majors, and 15% are science majors. Freshmen make up 32% of undergraduates. The percent of all freshmen enrolled in a freshman seminar is:

0.320.

A random sample of horses admitted to a local veterinary hospital found the following distribution of mares, geldings, and stallions: Sex mares geldings stallions Percent 0.51 0.44 0.05 The probability that a newly arriving horse at the veterinary hospital is a male is:

0.49.

A randomly selected sample of 100 horse owners found that 72 of them feed two flakes of grass hay in the morning and one flake of alfalfa plus one flake of grass hay in the evening to their horses. The estimated probability that horse owners feed grass hay in the A.M. and alfalfa plus grass hay in the P.M. is:

0.72.

At a large midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The mean of X is:

0.8.

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. If 10 horses are admitted during July, what is the probability at least one of the 10 horses has been infected with West Nile virus?

0.803

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. If 10 horses are admitted during July, what is the probability that 2 or fewer horses among the 10 horses admitted have been infected with West Nile virus?

0.8202

At a large midwestern college, 4% of the students are Hispanic. A random sample of 20 students from the college is selected. Let X denote the number of Hispanics among them. The standard deviation of X is:

0.88.

A group of freshmen at a local university consider joining the equestrian team. Students choose Western riding with probability P = 0.35, dressage with probability P = 0.45, and jumping with probability P = .40. The probability that a student chooses both dressage and jumping is P = 0.15, while the probability of a student choosing Western and dressage is P = 0.10. No one chooses Western and jumping. There are no horses suitable for both and each student is assigned to one horse. If five students decide to join the team, what is the probability that at least one student joins the dressage team?

0.9497

A system has two components that operate in parallel, as shown in the following diagram. Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probabilities of failures for the components 1 and 2 during one period of operation are 0.20 and 0.03, respectively. Let F1 denote the event that component 1 fails during one period of operation, and F2 denote the event that component 2 fails during one period of operation. The component failures are independent. The probability that the system functions properly during one period of operation is closest to:

0.994.

Assume that you are about to buy a car. There is a probability of 0.4 that you will purchase a new vehicle, and a probability of 0.5 that you will purchase a used vehicle. There is no probability that you will go home with more than one vehicle. The probability of the set of all outcomes is:

Suppose we are testing the null hypothesis H0: μ = 20 and the alternative Ha: μ 20, for a normal population with σ = 5. A random sample of 25 observations are drawn from the population, and we find the sample mean of these observations is = 17.6. The P-value is closest to:

.0164.

An SRS of size n0 was taken to estimate mean body mass index (BMI) for girls between 13 and 19 years of age. The 95% confidence interval obtained had lower limit 19.5 and upper limit 26.3. Which statement is NOT true?

A total of 95% of all teenage girls have BMI between 19.5 and 26.3.

Veterinary researchers at a major university veterinary hospital calculated a 99% confidence interval for the average age of horses admitted for laminitis, a foot disease that leaves the horse severely lame, as 6.3 to 7.4 years. This confidence intervals tells us that

All of the above

Which is an acceptable statement of a null and alternative hypothesis for testing a hypothesis about a mean?

All of the above

An assignment of probabilities to events in a sample space must obey which of the following?

All of the answer choices are correct.

A veterinary researcher takes an SRS of 60 horses presenting with colic. The average age of the 60 horses with colic is 12 years. The average age of horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of horses coming to the veterinary clinic is 8 years. After making a histogram of the ages of the horses with colic, the researcher finds a skewed distribution. Which statement is NOT true?

Decreasing the sample size has no effect on the sampling distribution of the sample mean.

The mean area μ of the several thousand apartments in a new development by a certain builder is advertised to be 1100 square feet. A tenant group thinks this is inaccurate, and suspects that the actual average area is less than 1100 square feet. In order to investigate this suspicion, the group hires an engineer to measure a sample of apartments to verify its suspicion. The appropriate null and alternative hypotheses, H0 and Ha, for μ are:

H0: μ = 1100 and Ha: μ < 1100.

Is the mean age at which American children can first read now under 4 years? If the population of all American children has mean age of μ years until they begin to read, one would test which null and alternative hypotheses to answer this question?

H0: μ = 4 vs. Ha: μ < 4

A statistician wishing to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The average score of the students on the exam was 78%. The hypothesis the statistician wants to test is:

H0: μ = 75 vs. Ha: μ > 75.

Which question can be used to draw conclusions from a test of significance?

If the P-value is less than the significance level α, then reject the null hypothesis.

A deck of cards is shuffled and you choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe its color, and replace it in the set. This process is repeated until you get a red card with X denoting the number of draws required. The random variable X has which probability distribution?

None of the above

Suppose we toss a fair coin repeatedly. We continue to do this until a "tail" is observed. Let X be the number of tosses required. Then X has a binomial distribution, with:

None of the above

The leading veterinarian at a local veterinary hospital decides to investigate whether there is an increase in West Nile virus infection in horses in the area. The horses diagnosed with West Nile infection are counted for the period April 15 through July 15. If X represents that count, a possible distribution for X is given by a:

None of the above

Which is an acceptable statement of a null and alternative hypothesis about a mean?

None of the above

A stack of four cards contains two red cards and two black cards. I select two cards, one at a time, and do not replace the first card selected before selecting the second card. Consider the events A = the first card selected is red B = the second card selected is red The events A and B are:

None of the answer choices is correct.

Event A occurs with probability 0.1. Event B occurs with probability 0.6. If A and B are independent, then:

P(A or B) = 0.64.

A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that preferred either dubstep or trance is calculated by;

P(A) + P(B) - P(A and B).

If a hypothesis test is significant at level α = 0.05, then what is known for the P-value?

P-value ≤ 0.05

Suppose that two very large companies (A and B) each select random samples of their employees. Company A has 5000 employees and Company B has 15,000 employees. In both surveys, the company will record the number of sick days taken by each sampled employee. If each company randomly selects 50 employees for the survey, which statement is TRUE about the sampling distributions of the sample means (the mean number of sick days)?

The sampling distributions of the sample means will have about the same standard deviation. The standard deviation for a sampling distribution of a sample mean depends only on the sample size, not the population (company) size.

Which statement is NOT true about the binomial distribution?

The smallest value can be zero or an integer above zero.

A North American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green. Suppose you decide to bet on red on each of 10 consecutive spins of the roulette wheel. Suppose you lose all five of the first wagers. Which statement is TRUE?

What happened on the first five spins tells us nothing about what will happen on the next five spins.

Opinion polls find that 20% of American adults claim that they never have time to relax. Suppose you take a random sample of 200 American adults and count the number X in your sample that claim that they never have time to relax. Using the Normal approximation, the probability that X is at least 50 is:

about 0.038.

In a test of hypothesis, a small P-value provides evidence:

against the null hypothesis in favor of the alternative hypothesis.

The P-value measures the strength of evidence:

against the null hypothesis.

A statistician wishing to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The statistician does not have access to Normal tables and decides to use resampling methods and simulation to find the P-value. This approach allows the statistician to calculate an:

approximate P-value.

approximately Normal, mean 112, standard deviation 1.443.

The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. The distribution of the sample mean of the weights of cheese wedges is:

approximately Normal, mean 8.1, standard deviation 0.063.

Two students taking a multiple choice exam with 20 questions and four choices for each question have the same, incorrect answer on eight of the problems. The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4. If the student is guessing, it is reasonable to assume guesses for different problems are independent. The instructor for the class suspects the students exchanged answers. The teacher decides to present a statistical argument to substantiate the accusation. A possible model for the number of incorrect questions that agree is a:

binomial distribution with n = 8 and p = .25.

Event A occurs with probability 0.2. Event B occurs with probability 0.9. Events A and B:

cannot be disjoint.

A veterinary researcher takes an SRS of 60 horses presenting with colic. The average age of the 60 horses with colic is 12 years. The average age of horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of horses coming to the veterinary clinic is 8 years. After making a histogram of the ages of the horses with colic, the researcher finds a skewed distribution. The researcher decides there is no need to increase the sample size because the law of large numbers:

does not depend on the population distribution being either skewed or symmetric.

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. We may conclude that:

either A or B always occurs.

All confidence intervals have the form:

estimate ± margin of error.

I toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, that is, the probability of heads is 1/2 and the probability of tails is 1/2. This means that:

if I flip the coin many, many times, the proportion of heads will be approximately 1/2, and this proportion will tend to get closer and closer to 1/2 as the number of tosses increases.

Suppose the population standard deviation is σ = 5, an SRS of n = 100 is obtained, and the confidence level is chosen to be 98%. The margin of error for estimating a mean μ is given by 1.1650. To reduce the margin of error to 0.3883 you should:

increase the sample size nine fold.

If the confidence level is increased from 90% to 99% for an SRS of size n, the width of the confidence interval for the mean μ will:

increase.

A statistician wishing to test a hypothesis that students score at most 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The average score of the 20 students on the exam was 72% and the standard deviation in the population is known to be σ = 15%. The statistician calculates the test statistic to be -0.8944. If the statistician chose to do a two-sided alternative, the P-value would be calculated by finding the area to the:

left of -.8944 and doubling it.

not F1 or not F2.

A P-value is always computed assuming that the:

null hypothesis is true.

The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age of these residents is to be computed. We know the random variable has approximately a Normal distribution because:

of the central limit theorem.

population mean.

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 110 and standard deviation σ = 20. You suspect that incoming freshman have a mean μ, which is different from 110 because they are often excited yet anxious about entering college. To verify your suspicion, you test the hypotheses H0: μ = 110, Ha: μ 110 You give the SSHA to 50 students who are incoming freshman and find their mean score. The P-value of the test of the null hypothesis is the:

probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed.

A randomly selected sample of 100 horse owners found that 72 of them feed grass hay in the morning and alfalfa in the evening to their horses. The value 0.72 represents the:

proportion of horse owners in the sample that feed grass hay in the a.m. and alfalfa in the p.m.

When we draw a card from a deck, the outcome is uncertain. The card's value is:

random.

sample mean.

You toss a thumbtack 100 times and observe that it lands "point down" 65 times. The proportion of times it landed "point down" is then 0.65. This proportion represents the:

sample proportion of tosses that landed "point down" in your 100 tosses.

A hypothesis test consists of the following four steps:

state, plan, solve, conclude.

In a statistical test of hypotheses, we say the data are statistically significant at level α if:

the P-value is less than α.

A small class has 10 students. Seven of the students are male and three are female. You write the name of each student on a small card. The cards are shuffled thoroughly and you choose one at random, observe the name of the student, and replace it in the set. The cards are thoroughly reshuffled and you again choose a card at random, observe the name, and replace it in the set. This is done a total of five times. Let X be the number of cards observed in these four trials with a name corresponding to a male student. The random variable X has which probability distribution?

the binomial distribution, with parameters n = 5 and p = 0.7

For which count would a binomial probability model be reasonable?

the number of sevens in a randomly selected set of five random digits from your table of random digits

North American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green. If you bet on red, the probability of winning is 18/38 = 0.4737. The probability 0.4737 represents:

the proportion of times this event will occur in a very long series of individual bets on red.

I roll a four-sided die. The possible outcomes are 1, 2, 3, or 4, depending on the number of spots on the side of the die that is face down. This collection of all possible outcomes is called:

the sample space.

Suppose you interview 10 randomly selected workers and ask how many miles they commute to work. You'll compute the sample mean commute distance. Now imagine repeating the survey many, many times, each time recording a different sample mean commute distance. In the long run, a histogram of these sample means represents:

the sampling distribution of the sample mean.

In a test of statistical hypotheses, the P-value tells us:

the smallest level of significance at which the null hypothesis can be rejected.

we are 99% confident that the true mean age of horses with laminitis is between 6.3 and 7.4 years old.

Suppose you want to estimate the average number of sick days taken by all employees at a large company during a year. Suppose (unknown to you) this is four days. You devise a way to randomly select 200 employees for a survey and use the sample mean number of sick days as an estimate of the population mean for all workers at the company. Unknown to you, the sampling distribution of the sample mean has an average value of 4.8. This means that:

your estimator (the sample mean) is not an unbiased estimator of the population mean because your sampling method tends to pick people that take more sick days.

A 95% confidence interval for the mean hours freshmen spent on social media per day was calculated to be (2.5 hrs, 3.1 hrs). The confidence interval was based on an SRS of size n = 50. The standard deviation is given by

1.0823.

Suppose the population standard deviation is σ = 5, an SRS of n = 100 is obtained, and the confidence level is chosen to be 98%. The margin of error for estimating a mean μ is given by:

1.1650.

An SRS of 25 recent birth records at the local hospital was selected. In the sample, the average birth weight was = 119.6 ounces. Suppose the standard deviation is known to be σ = 6.5 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean μ. The standard deviation of the sampling distribution of the mean is:

1.30 ounces.

A set of 20 cards consists of 12 red cards and eight black cards. The cards are shuffled thoroughly and you choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe its color, and replace it in the set. This is done a total of six times. Let X be the number of red cards observed in these six trials. The variance of X is:

1.44.

The upper 0.05 critical value of the standard Normal distribution is:

1.645.

10%.

To calculate a 99% confidence interval, the value z* in the margin of error should equal:

2.576.

28.80.

In a particular game, a six-sided fair die is tossed. If the number of spots showing is a six, you win $6, if the number of spots showing is a five, you win $3, if the number of spots showing is 4, you win $2, and if the number of spots showing is 3, you win $1. If the number of spots showing is 1 or 2, you win nothing. You are going to play the game twice. The probability that you win something on each of the two plays of the game is:

4/9.

A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The proportion of students that didn't select any of the music options available on the survey was:

40%

40%.

Spelling mistakes in a text are either "nonword errors" or "word errors." A nonword error produces a string of letters that is not a word, such as "the" typed as "teh." Word errors produce the wrong word, such as "loose" typed as "lose." Nonword errors make up 25% of all errors. A human proofreader will catch 80% of nonword errors and 50% of word errors. What percent of errors will the proofreader catch?

57.5%

60%

A group of college DJs surveyed students to find out what music to plan for their upcoming parties. Thirty percent of the students preferred dubstep, 25% of the students liked trance music, and 20% wanted to hear only house music. Fifteen percent of the respondents selected both dubstep and trance. The conditional probability that a student likes dubstep given that he or she likes trance music is:

60%.

65.2%

Suppose that the population of the scores of all high school seniors that took the SAT-M (SAT math) test this year follows a Normal distribution, with mean μ and standard deviation σ = 100. You read a report that says, "On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for μ is 512.00 ± 25.76." The confidence level for this interval is:

99%

A random sample of n = 25 flights was taken and the time recorded to board the flight. It was found that minutes. Previous studies had determined boarding times to be normally distributed with μ = 38 minutes and σ = 36 minutes. The sampling distribution of , the sample average in samples of size n = 25 is:

N(38, 7.2).

You measure the lifetime of a random sample of 64 tires of a certain brand. In a follow-up study, more tires were available for testing, so you were able to measure the lifetimes of a random sample of 100 tires rather than 64. Which statement is TRUE?

The margin of error for our 99% confidence interval would decrease.

I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the proportion I observe from the population. Which of the following would produce a new confidence interval with smaller width (smaller margin of error) based on these same data?

Use a smaller confidence level.

A level 0.95 confidence interval is:

a range of values computed from sample data that will contain the true value of the parameter of interest 95% of the time.

In formulating hypotheses for a statistical test of significance, the null hypothesis is often:

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