Stats exam
Suppose that you are a student worker in the statistics department and agree to be paid according to the "random pay" system. Each week, the chair of the department flips a coin. If the coin comes up heads, your pay for the week is $80. If it comes up tails, your pay for the week is $40. You work for the department for 100 weeks (at which point you have learned enough probability to know that the "random pay" system is not to your advantage). The probability that X bar, your average earnings in the first two weeks, is greater than $65 is
.2500 Equal to probability of getting 2 heads 2 times
As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a package of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as independent trials. Let p hat be the sample proportion of the next 100 shoppers that buy a package of crackers after tasting a free sample. The probability that fewer than 30% of these individuals buy a package of crackers after tasting a sample is approximately (without using the continuity correction)
.9938 (.3-.2)÷square root((.2×.8)÷100)
In a certain large population, 70% are right-handed. You need a left-handed pitcher for your softball team and decide to find one by asking people chosen from the population at random. (We assume that once you do find a left-hander, he or she will be happy to join your team and will not say no.) The probability that the first left-hander you find is the fourth person you ask is approximately
0.1029
In a certain large population, 70% are right-handed. You need a left-handed pitcher for your softball team and decide to find one by asking people chosen from the population at random. (We assume that once you do find a left-hander, he or she will be happy to join your team and will not say no.) The probability that you will have to ask at most two people to find your first left-hander is approximately
0.51 .7×.3=.21 + .3=.51 OR 1-(1-.3)^2
The duration of Alzheimer's disease, from the onset of symptoms until death, ranges from 3 to 20 years, with a mean of 8 years and a standard deviation of 4 years. The administrator of a large medical center randomly selects the medical records of 30 deceased Alzheimer's patients and records the duration of the disease for each one. Find the probability that the average duration of the disease for the 30 patients will lie within 1 year of the overall mean of 8 years.
0.8294 Use s.d.=4/square root 30 = 4/0.73
The duration of Alzheimer's disease, from the onset of symptoms until death, ranges from 3 to 20 years, with a mean of 8 years and a standard deviation of 4 years. The administrator of a large medical center randomly selects the medical records of 30 deceased Alzheimer's patients and records the duration of the disease for each one. Find the value L such that there is a probability of 0.99 that the average duration of the disease for the 30 patients lies less than L years above the overall mean of 8 years.
1.70
We wish to test H0: μ = 10 against Ha: μ > 10, where μ is the unknown mean of a normal population for which the standard deviation σ is also unknown. We draw an SRS of size n = 13 from the population and compute the value of the test statistic, t. From the table of critical values of the t distribution, find the critical value t* that we would compare against the value of t to make a decision about the significance of the test results at significance level α = 0.05.
1.782
To assess the accuracy of a kitchen scale, a standard weight, known to weigh 1 gram, is weighed a total of n times, and the mean x bar of the n weight measurements is computed. Suppose the scale readings are normally distributed with unknown mean μ and standard deviation σ = 0.01 gram. How large should n be so that a 90% confidence interval for μ has a margin of error of E = ± 0.0001 gram?
27,061
A noted psychic is tested for ESP. The psychic is presented with 400 cards, all face down, and asked to determine whether each card is marked with one of four symbols: a star, a cross, a circle, or a square. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. How many trials would you need to conduct to estimatep to within ± 0.01 ("plus or minus one percentage point") with 95% confidence? (Use the guess 0.25 as the value for p. Note that this would be the value of p if the psychic were merely guessing.)
7203
Suppose that we are given random variables X, Y for which we know the means μX, μY and the variances σ2X, σ2Y. Which of the following quantities could we not compute without knowing some additional information about X, Y?
C A. μX - Y B. μ3X - 2Y C. σX+Y
In a simple random sample of 1000 Americans, it was found that 61% were satisfied with the service provided by the dealer from which they bought their car. In a simple random sample of 1000 Canadians, 58% said that they were satisfied with the service provided by their car dealer. Which of the following statements concerning the sampling variability of these statistics is true?
The sampling variability is about the same in both cases
Agricultural researchers plant 100 plots with a new variety of corn. The average yield for these plots is x bar = 130 bushels per acre. Assume that the yield per acre for the new corn variety follows a normal distribution with unknown mean μ and standard deviation σ = 10 bushels per acre. A 90% confidence interval for μ is a. 130 ± 1.645 b. 130 ± 16.45 c. 130 ± 1.96
a.
For which of the following choices of n, p can we not use the normal approximation to the binomial distribution? a. n = 60, p = 0.9 b. n = 40, p = 0.4 c. n = 25, p = 0.6
a.
Which of the following is not a property of the Student's t distribution? a. The density curve of the t distribution more closely resembles the density curve of the standard normal distribution when the number of degrees of freedom is small. b. The density curve of the t distribution has thicker "tails" than the density curve of the standard normal distribution. c. The density curve of the t distribution is symmetric about 0.
a.
Which of the following probability distributions of a discrete random variable X is not a legitimate distribution? a. X -1 0 1 P(X) 0.2 0.2 0.5. b. X -1 0 1 P(X) 0.3 0.4 0.3 c. X 1 2 3 P(X) 0.3 0.3 0.4
a.
A radio talk show host is interested in the proportion p of adults in his listening area who think that the drinking age should be lowered to 18. To find this proportion, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to 18 in light of the fact that 18-year-olds are eligible for military service?" He asks listeners to phone in and vote "yes" or "no" depending upon their opinions. Of 200 people who phone in, 140 answer "yes." The standard error of the sample proportion p hat of "yes" votes among those who phone in is
a. 0.032 Square root (.7×.3)÷200
A manufacturer receives parts from two suppliers. An SRS of 400 parts from Supplier 1 contains 20 defectives, while an independent SRS of 100 parts from Supplier 2 contains 10 defectives. Let p1 and p2 be the proportions of defectives for all parts made by Supplier 1 and Supplier 2, respectively. Is there evidence of a significant difference in the proportions of defective parts made by these two suppliers? To answer this question, you test the hypotheses H0: p1 = p2 , Ha: p1 ≠p2. The P-value of the test is
a. 0.0602
Independent random samples of 9 observations from each of two normally distributed populations are taken and the following results obtained: Sample from population 1: 10.2, 10.6, 10.7, 10.4, 10.5, 10, 10.2, 10.7, 10.4 Sample from population 2: 9.9, 9.4, 9.3, 9.6, 10.2, 10.6, 10.3, 10, 10.3 The sample standard deviations are found to be s1 ≈ 0.242 and s2 ≈ 0.445. What is the standard error of the sample mean difference x bar 1 minus x bar 2? a. 0.169 b. 0.229 c. 0.056
a. 0.169
Jamaal, a player on a college basketball team, made only 50% of his free throws last season. During the off-season, he worked on developing a softer shot in the hope of improving his free-throw accuracy. This season, Jamaal made 54 of 95 free throws. Can we conclude that Jamaal's free-throw percentage p this season is significantly different from last year's percentage? The approximate P-value for an appropriate test is a. 0.1836. b. 0.8164. c. 0.0918.
a. 0.1836
The time in minutes X that you must wait before a train arrives at your local subway station is a uniformly distributed random variable between 5 minutes and 15 minutes. That is, the density curve of the distribution of x has constant height between 5 and 15 and height 0 outside this interval. Determine P(6 < X < 8).
a. 0.2
In a certain large population, 70% are right-handed. You need a left-handed pitcher for your softball team and decide to find one by asking people chosen from the population at random. (We assume that once you do find a left-hander, he or she will be happy to join your team and will not say no.) The probability that you will have to ask more than three people before finding your first left-hander is approximately
a. 0.343 (1-.3)^3 (1-p)^n
Let X = the number of times that a customer visits a grocery store during a one-week period. Assume that the probability distribution of X is as follows: X 0 1 2 3 P(X) 0.1 0.4 0.4 0.1 The standard deviation of X, σX, is approximately
a. 0.81 1-var stats (L1,L2)
We want to use the t test for a population mean difference μd to test the claim H0: μd = 1. For five paired observations, the differences are 4, -1, 4, 0, and 3. The approximate value of the test statistic in this case is a. 0.95. b. 1.91. c. 2.13.
a. 0.95
There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The student's expected (mean) score on this exam is
a. 25
Suppose we have a "loaded" (unfair) die that gives the outcomes 1 through 6 according to the probability ditribution X 1 2 3 4 5 6 P(X) 0.1 0.2 0.3 0.2 0.1 0.1 If this die is rolled 6000 times, then the sample mean number of spots per roll for the 6000 rolls should be about
a. 3.30
You are thinking of using the t test to test a hypothesis about the mean of a population. A random sample of size n from the population has a slightly skewed distribution with no apparent outliers. For which of the following sample sizes n could you not justify using the t test? a. 5 b. 20 c. neither (A) nor (B). We can justify using the t test in either case.
a. 5
There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The standard deviation of the student's score on the exam is
a. 9.68
Which of the following will cause the power of a test to increase? a. increasing the sample size. b. increasing the probability of committing a Type II error, β c. decreasing the significance level α of the test
a. Increasing the sample size
In a statistics class containing 250 students, each student is instructed to toss a coin 20 times and record the value of p hat, the sample proportion of heads. The instructor then makes a histogram of the 250 values of p hat obtained. In a second statistics class containing 200 students, each student is told to toss a coin 40 times and record the value of p hat, the sample proportion of heads. The instructor then makes a histogram of the 200 values of p hat obtained. Which of the following statements regarding the two histograms of p hat values is true? a. The first class's histogram has greater spread (variability) since it is derived from a smaller number of tosses per student. b. The first class's histogram is more biased since it is derived from a smaller number of tosses per student. c. The first class's histogram has less spread (variability) since it is derived from a larger number of students.
a. The first class's histogram has greater spread (variability) since it is derived from a smaller number of tosses per student.
Suppose we conduct a test of hypotheses and find that the test results are significant at level α = 0.025. Which of the following statements then must be true? a. The results are significant at level α = 0.05. b. The test results are important. c. The results are not significant at level α = 0.01.
a. The results are significant at level α = 0.05.
We wish to see whether the dial temperature for a certain model oven is properly calibrated. Four ovens of a certain model are selected at random. The dial on each oven is set to 300°F. After one hour, the actual temperature of each oven is measured. The observed temperatures are 305°, 310°, 300°, and 305°. Assuming that actual temperatures for this model when the dial is set to 300° are normally distributed with mean μ, we test to see whether the oven is properly calibrated by testing H0: μ = 300 against a two-sided alternative. From the data, the P-value for this test is a. between 0.05 and 0.10. b. between 0.025 and 0.05. c. between 0.01 and 0.025.
a. between 0.05 and 0.10
A social psychologist reports that "in our sample, ethnocentrism was significantly higher (P < 0.05) among church attendees than among nonattendees." This means that a. if there were actually no difference in ethnocentrism between church attendees and nonattendees, then the chance that we would have observed a difference at least as extreme as the one we did is less than 5%. b. ethnocentrism was at least 5% higher among church attendees than among nonattendees. c. the observed differences between church attendees and nonattendees account for all but 5% of those sampled. These results are quite meaningful and should be investigated further.
a. if there were actually no difference in ethnocentrism between church attendees and nonattendees, then the chance that we would have observed a difference at least as extreme as the one we did is less than 5%.
A widget manufacturer estimates that the total weekly cost in dollars, C, to produce x widgets is given by the linear function C(x) = 500 + 10x, where the intercept 500 represents a "fixed" cost of manufacture and the slope 10 represents the "variable" cost of producing a certain number of widgets. Analysis of weekly widget production reveals that the number of widgets X produced in a week is a random variable with mean μX = 200 and standard deviation σX = 20. What are the mean and the standard deviation of C?
a. mean of C = $2500, standard deviation of C = $200 ((10^2)×(20^2))^(1÷2)=200
A news magazine claims that 30% of all New York City police officers are overweight. Indignant at this claim, the New York City police commissioner conducts a survey in which 200 randomly selected New York City police officers are weighed. 52, or 26%, of the surveyed officers turn out to be overweight. Which of the following statements about this situation is true? a. The number 26% is a parameter. b. The number 26% is a statistic. c. The number 30% is a statistic.
b.
A random sample of size n is collected from a normal population with standard deviation σ. Using these data, a confidence interval is computed for the mean of the population. Which of the following actions would produce a new confidence interval with a smaller width (smaller margin of error), assuming that the same data were used? a. using a smaller sample size n b. using a lower confidence level c. increasing the value of σ
b.
The heights (in inches) of adult males in the United States are believed to be normally distributed with mean μ. The average height of a random sample of 25 American adult males is found to be x bar = 69.72 inches, with a sample standard deviation of s = 4.15 inches. A 90% confidence interval for μ is a. 69.72 ± 1.37. b. 69.72 ± 1.42. c. 69.72 ± 1.09.
b.
Which of the following P-values obtained from a test of hypotheses constitutes the least amount of evidence against the null hypothesis? a. 0.107 b. 0.207 c. 0.017
b.
Suppose that we have a deck of three cards, one marked with a 1, one marked with a 2, and one marked with a 5. You draw two cards at random and without replacement from the deck. The sample space S = {(1, 2), (1, 5), (2, 5)} consists of these three equally likely outcomes. Let X be the sum of the numbers on the two cards drawn. Which of the following is the correct probability distribution for X?
b. X 3 6 7 P(X) 1/3 1/3 1/3
In a particular game, a ball is randomly chosen from a box that contains 3 red balls, 1 green ball, and 6 blue balls. If a red ball is selected, you win $2; if a green ball is selected, you win $4; if a blue ball is selected, you win nothing. Let X be the amount that you win. The expected value of X is
b. $1
A noted psychic is tested for ESP. The psychic is presented with 400 cards, all face down, and asked to determine if each card is marked with one of four symbols: a star, a cross, a circle, or a square. The psychic is correct in 120 of the 400 cases. Let prepresent the probability that the psychic correctly identifies the symbol on the card in a random trial. Suppose we wish to see if there is evidence to suggest that the psychic is doing significantly better than he would be if he were just guessing. To do so, we test H0: p = 0.25 against Ha: p > 0.25. The P-value of the test is a. 0.9896. b. 0.0104. c. 0.0146.
b. 0.0104
The daily total sales (excepting Saturday) at a small restaurant has a probability distribution that is approximately normal with a mean of μ = $530 and a standard deviation of σ = $120. The probability the sales will exceed $700 on a given day is approximately
b. 0.0778
There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. If the student needs at least 40 points to pass the exam, the probability that she passes is closest to
b. 0.1018 1-binomcdf (20, .25, 7)
Let X = the number of times that a customer visits a grocery store during a one-week period. Assume that the probability distribution of x is as follows: X 0 1 2 3 P(X) 0.1 0.4 0.4 0.1 Use the distribution to determine the probability that a randomly chosen customer visits the grocery store at least twice during a one-week period.
b. 0.5
The weight of a medium-sized orange selected at random from a large bin of oranges at a local supermarket is a random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. Suppose we independently select two oranges at random from the bin. The difference in the weights of the two oranges (the weight of the first orange minus the weight of the second orange) is a random variable with a standard deviation equal to
b. 1.70 ounces 1.2^2 + 1.2^2
In the old children's game of "rock?scissors?paper," two players simultaneously use their hands to show one of three objects: a rock (a closed fist), a pair of scissors (two fingers extended in a V-shape), or a piece of paper (an open palm). The winner is chosen in the following ways: Rock beats scissors (rock can crush scissors). Scissors beats paper (scissors can cut paper). Paper beats rock (paper can wrap around rock). If the players each show the same object, then the game is played again, with additional repeats as needed until one player wins. Assume that each player selects an object independently and that each player is equally likely to choose any of the three objects. Let X = the number of games that must be played in order to decide a winner. (We assume that the identity of the winner is unimportant). Then X is a geometric random variable with probability of success p equal to
b. 2/3
A researcher collects infant mortality data from a random sample of villages in a certain country. It is claimed that the average death rate in this country is the same as that of a neighboring country, which is known to be 17 deaths per 1000 live births. To test this claim using a test of hypotheses, what should the null and alternative hypotheses be? a. H0: μ ≠ 17, Ha: μ = 17 b. H0: μ = 17, Ha: μ ≠ 17 c. H0: μ = 17, Ha: μ > 17
b. H0: μ = 17, Ha: μ ≠ 17
The time that it takes an untrained rat to run a standard maze has a normal distribution with mean 65 seconds and standard deviation 15 seconds. The researchers want to use a test of hypotheses to determine whether training significantly improves the rats' completion times. An appropriate alternative hypothesis would have the form
b. Ha: μ < 65.
Consider the following set of random variables: I. Total number of points scored during a football game II. Lifespan in hours of a halogen light bulb III. Height in feet of the ocean's tide at a given location IV. Number of fatalities in civilian aircraft crashes in a given year V. Length in inches of an adult rattlesnake. Which ones are continuous random variables?
b. II, III, and V only
Suppose that we would like to test H0: μ = 50 against Ha: μ ≠ 50, where μ is the mean of a normal population, using a test based on the standard normal distribution. The 95% confidence interval for μ is found to be (51.3, 54.7). Which of the following must then be true? a. The P-value of the test is greater than 0.05. b. The P-value of the test is at most 0.05. c. The P-value of the test could be either greater than or at most 0.05. It can't be determined without knowing the sample size.
b. The P-value of the test is at most 0.05
A researcher wishes to compare the effects of two stepping heights (low and high) on heart rate in a step-aerobics workout. A sample of 50 adults in roughly similar physical condition was randomly divided into two groups of 25 subjects each. Group 1 did a standard step-aerobics workout using the low stepping height. The sample mean heart rate at the end of Group 1's workout was x bar 1= 90 beats per minute (bpm), with a sample standard deviation of s1 = 9 bpm. Group 2 did the same workout but used the high stepping height. The sample mean heart rate at the end of Group 2's workout was x bar 2= 95.08 bpm, with a sample standard deviation of s2 = 12 bpm. Assume that the two sets of data are independently generated and that both data distributions are approximately normal. Let μ1 and μ2represent the mean heart rates we would observe for the entire population of interest if all members of the population did the workout using the low and high stepping height, respectively. Suppose that the researcher wishes to test the hypotheses H0: μ1 = μ2, and Ha: μ1 < μ2. Using the conservative value for the number of degrees of freedom, the P-value of the test is a. between 0.01 and 0.05. b. between 0.05 and 0.10. c. larger than 0.10.
b. between 0.05 and 0.10
The scores of individual students on the American College Testing (ACT) program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the ACT test. If the scores at this school have the same distribution as the national scores, then the sampling distribution of the average (sample mean) score x bar for these 36 students is a. approximately normal, but the approximation is poor. b. exactly normal. c. approximately normal, but the approximation is good.
b. exactly normal
In a certain large population, 70% are right-handed. You need a left-handed pitcher for your softball team and decide to find one by asking people chosen from the population at random. (We assume that once you do find a left-hander, he or she will be happy to join your team and will not say no.) The mean and variance of the number of people you will have to ask to find your first left-hander are
b. mean = 3.33, variance = 7.78 mean=1÷0.3 variance=(1-0.3)÷(0.3^2)
A set of 10 playing cards consists of 5 red cards and 5 black cards. The cards are shuffled thoroughly, and we draw 4 cards one at a time and without replacement. Let X = the number of red cards drawn. The random variable X has which of the following probability distributions? a. binomial distribution with parameters n = 10 and p = 0.5 b. binomial distribution with parameters n = 4 and p = 0.5 c. neither (A) nor (B)
c
A random sample of 85 students in Chicago's city high schools take a course designed to improve SAT scores. Based on this sample, a 90% confidence interval for the mean improvement μ in SAT score for all Chicago city high school students taking this course is found to be (72.3, 91.4). Which of the following statements is the correct interpretation of this interval? a. Ninety percent of the students in the sample improved their scores by between 72.3 and 91.4 points. b. Ninety percent of the students in the population who take the course should improve their scores by between 72.3 and 91.4 points. c. Neither (A) nor (B) is correct.
c.
An inspector inspects large truckloads of potatoes to determine the proportion p of potatoes with major defects prior to using the potatoes to make potato chips. She intends to compute a 95% confidence interval for p. To do so, she selects an SRS of 50 potatoes from a truckload of over 2000 potatoes. Suppose that only 2 of the 50 potatoes sampled are found to have major defects. Which of the following assumptions for inference about a proportion using a confidence interval are violated? a. There appear to be no violations. b. The population is at least 10 times as large as the sample. c. The sample size n is large enough that both the count of successes np'hat' and the count of failures n(1 - p'hat') are 10 or more.
c.
Do students tend to improve their SAT Mathematics (SAT-M) score the second time they take the test? Four randomly sampled students who took the test twice received the following scores: Student 1 / 2 / 3 / 4 First score 450 / 520 / 720 / 600 Second score 440 / 600 / 720 / 630 Assume that the change in SAT-M score (= second score - first score) for the population of all students taking the test twice is normally distributed with mean μd. A 95% confidence interval for μd is a. 25.0 ± 56.09. b. 25.0 ± 39.60. c. 25.0 ± 64.29.
c.
One hundred rats whose mothers were exposed to high levels of tobacco smoke during pregnancy were put through a simple maze. At the outset, the maze required the rats to make a choice between going left and going right. Eighty of the rats went right when running the maze for the first time. Assume that the 100 rats can be considered an SRS from the population of all rats born to mothers who were exposed to high levels of tobacco smoke during pregnancy. (Note that this assumption may or may not be reasonable, but researchers often assume that lab rats are representative of large populations, since they are often bred to have uniform characteristics.) Let p be the proportion of rats in this population that would go right when running the maze for the first time. A 90% confidence interval for p is a. 0.8 ± 0.078. b. 0.8 ± 0.040. c. 0.8 ± 0.066.
c.
As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a package of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as independent trials. Let p hat be the sample proportion of the next 100 shoppers that buy a package of crackers after tasting a free sample. Which of the following best describes the sampling distribution of the statistic p hat? a. It cannot be approximated by a normal distribution. b. It is approximately normal with mean μ p hat = 0.2 and standard deviation σ p hat = 0.0016. c. It is approximately normal with mean μ p hat = 0.2 and standard deviation σ p hat = 0.04.
c. mean=p s.d.=square root ((p×(1-p))÷n)
There are 20 multiple-choice questions on an exam, each having four possible responses, of which only one is correct. Each question is worth 5 points if answered correctly. Suppose that a student guesses the answer to each question, with her guesses from question to question being independent. The probability that the student scores lower than a 60 on the exam is
c. .9991 Binomcdf (20, .25, 11)
For a simple random sample of 100 cars of a certain popular model in 2003, it was found that 20 had a certain minor defect in the brakes. For an independent SRS of 400 cars of the same model in 2004, it was found that 50 had the same defect. Let p1 and p2 be the proportions of all cars of this model in 2003 and 2004, respectively, that have the defect. A 90% confidence interval for p1 - p2 is (approximately) a. 0.075 ± 0.043. b. 0.075 ± 0.085. c. 0.075 ± 0.071.
c. 0.075 ± 0.071
The daily total sales (excepting Saturday) at a small restaurant has a probability distribution that is approximately normal with a mean of μ = $530 and a standard deviation of σ = $120. The probability the sales will exceed $700 on a given day is approximately
c. 0.0778
A sociologist is studying the effect on the divorce rate of having children within the first three years of marriage. She selects a random sample of 400 couples who were married for the first time between 1990 and 1995 with both members of the couple aged 20 to 25. Of the 400 couples, 220 had at least one child within the first three years of marriage. Of the couples who had children, 83 were divorced within five years, while of the couples who didn't have children, 52 were divorced within five years. Let p1 and p2 be the proportions of couples married in this time frame and divorced within five years who had children and didn't have children, respectively. From the data, the estimate of p1 - p2 is
c. 0.0884
We want to use the t test for a population mean difference μd to test the claim H0: μd = 1. For five paired observations, the differences are 4, -1, 4, 0, and 3. The approximate value of the test statistic in this case is a. 2.13. b. 1.91. c. 0.95.
c. 0.95.
As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a package of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as independent trials. Let p hat be the sample proportion of the next n shoppers that buy a packet of crackers after tasting a free sample. How large should n be so that the standard deviation of p hat is no more than 0.01? a. 16 b. 4 c. 1600
c. 1600
Some agricultural researchers have conjectured that stem-pitting disease in peach tree seedlings might be controlled through weed and soil treatments. An experiment was conducted to compare seedling growth with soil and weeds treated with one of two herbicides. In a field containing 10 seedlings, 5 were randomly selected and assigned to be treated with Herbicide A; the remaining 5 seedlings were treated with Herbicide B. Soil and weeds for each seedling were treated with the appropriate herbicide. At the end of the study period, the height (in centimeters) was recorded for each seedling. A 90% confidence interval for the difference μA - μB in mean seedling height for the two herbicides was found to be (0.2, 14.6). From this result, which of the following statements is correct? a. The P-value for a test of H0: μA = μB against Ha: μA ≠ μB would be greater than 0.10, since the interval doesn't contain 0. b. A 95% confidence interval would not include 0 either, since we would be even more confident that a significant difference exists between the two groups. c. Neither (A) nor (B) is correct.
c. Neither (A) nor (B) is correct
Suppose that we are conducting a test for a population mean μ based on the standard normal distribution. We originally do a one-sided test but then decide that a two-sided test might be more appropriate (typically, we prefer to use a two-sided test unless there is some reason to believe that an effect in a particular direction exists). How will the results of the test change if we use a two-sided test instead of a one-sided test, assuming that the same data are used? a. The P-value of the test will be smaller. b. The test statistic will have a larger value. c. We will require stronger evidence against H0 to reject H0.
c. We will require stronger evidence against H0 to reject H0.
The Department of Health plans to test the lead level in a public park. The park will be closed if the lead level exceeds the allowed limit; otherwise, the park will be kept open. The department conducts the test using soil samples gathered at randomly selected locations. Which of the following decisions would constitute making a Type I error in this situation? a. keeping the park open when the average lead level exceeds the allowed limit b. closing the park when the average lead level exceeds the allowed limit c. closing the park when the average lead level is acceptable
c. closing the park when the average lead level is acceptable
In a test of hypotheses, the probability that a false null hypothesis should be rejected is also known as the a. probability of committing a Type II error b. significance level of the test. c. power of the test.
c. power of the test. (Actually the probability of avoiding a Type 2 error and probability of correctly rejecting the null)
In the gambling game of chuck-a-luck, three dice are rolled using a rotating, hourglass-shaped cage. The player chooses one of the 6 possible sides (1, 2, 3, 4, 5, or 6) and receives a payoff the amount of which depends on how many dice turn up on that particular side. LetX = the number of times the dice have to be rolled until we see "three of a kind" (of any type). Which of the following probability distributions does X have?
geometric with p=6/216
