Stats 128
Analyze the residual plot below and identify which, if any, of the conditions for an adequate linear model is not met.
Dots everywhere. None.
In a certain card game, the probability that a player is dealt a particular hand is 0.42. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 42 times? Why or why not?
B. The probability 0.42 means that approximately 42 out of every 100 dealt hands will be that particular hand. No, you will not be dealt this hand exactly 42 times since the probability refers to what is expected in the long-term, not short-term.
Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axis are the same for each scatter diagram. (a) r = -1, (b) r = -0.049, (c) r = -0.992
(a) = II, straight line down (b) = III, dots everywhere (c) = II, wider line down
Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. The correlation coefficient is 0.858 and the least squares regression line is Y = 0.264x + 10.256 Complete parts (a) through (c) below.
(a) Compute the coefficient of determination, r^ = 73.6% (Round to one decimal place as needed.) (c) Interpret the coefficient of determination and comment on the adequacy of the linear model. Approximately 73.6% of the variation in head circumference is explained by the least-squares regression model. According to the residual plot, the linear model appears to be appropriate.
According to an airline, flights on a certain route are on time 85% of the time. Suppose 10 flights are randomly selected and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Determine the values of n and p. (c) Find and interpret the probability that exactly 7 flights are on time. (d) Find and interpret the probability that fewer than 7 flights are on time. (e) Find and interpret the probability that at least 7 flights are on time. (f) Find and interpret the probability that between 5 and 7 flights, inclusive, are on time.
(a) Identify the statements that explain why this is a binomial experiment. Select all that apply. A. The probability of success is the same for each trial of the experiment. C. There are two mutually exclusive outcomes, success or failure. E. The experiment is performed a fixed number of times. G. The trials are independent. (b) nequals 10 (Type an integer or a decimal. Do not round.) pequals 0.85 (Type an integer or a decimal. Do not round.) (c) The probability that exactly 7 flights are on time is 0.1298. (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected that about 13 will result in exactly 7 flights being on time. (Round to the nearest whole number as needed.) (d) The probability that fewer than 7 flights are on time is 0.0500. (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected that about 5 will result in fewer than 7 flights being on time. (Round to the nearest whole number as needed.) (e) The probability that at least 7 flights are on time is 0.9500. (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected that about 95 will result in at least 7 flights being on time. (Round to the nearest whole number as needed.) (f) The probability that between 5 and 7 flights, inclusive, are on time is 0.1784. (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected that about 18 will result in between 5 and 7 flights, inclusive, being on time. (Round to the nearest whole number as needed.)
The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years. Complete parts (a) through (e). Weapon Probability Handgun 0.475 Rifle 0.027 Shotgun 0.034 Unknown firearm 0.142 Knives 0.133 Hands, fists, etc. 0.057 Other 0.132
(a) Is the given table a probability model? Why or why not? D. Yes; the rules required for a probability model are both met. (b) What is the probability that a randomly selected murder resulted from a rifle or shotgun? P(rifle or shotgun)equals 0.061 (Type a decimal rounded to three decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box to complete your choice. A. If 1000 murders were randomly selected, we would expect about 61 of them to have resulted from a rifle or shotgun. (c) What is the probability that a randomly selected murder resulted from a handgun, rifle, or shotgun? P(handgun, rifle, or shotgun)equals 0.536 B. If 1000 murders were randomly selected, we would expect about 536 of them to have resulted from a handgun, rifle, or shotgun. (d) What is the probability that a randomly selected murder resulted from a weapon other than a gun? P(weapon other than a gun)equals 0.322 A. If 1000 murders were randomly selected, we would expect about 322 of them to be have resulted from a weapon other than a gun. (e) Are murders with a shotgun unusual? Yes
A bag of 100 tulip bulbs purchased from a nursery contains 40 red tulip bulbs, 20 yellow tulip bulbs, and 40 purple tulip bulbs. (a) What is the probability that a randomly selected tulip bulb is red? (b) What is the probability that a randomly selected tulip bulb is purple? (c) Interpret these two probabilities.
(a) The probability that a randomly selected tulip is red is 0.4. (Type an integer or a decimal. Do not round.) (b) The probability that a randomly selected tulip bulb is purple is 0.4. (Type an integer or a decimal. Do not round.) B. If 100 tulip bulbs were sampled with replacement, one would expect about 40 of the bulbs to be red and about 40 of the bulbs to be purple.
On an international exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in the exam, the correlation between the percentage of items answered in the background questionnaire (used as a proxy for student task persistence) and mean score on the exam was 0.728. Does this suggest there is a linear relation between student task persistence and achievement score? Write a sentence that explains what this result might mean. Does this suggest there is a linear relation between student task persistence and achievement score? Choose the best response below. What does this result mean?
A. Yes, since |0.728| is greater than the critical value for 30. B. Countries in which students answered a greater percentage of items in the background questionnaire tended to have higher mean scores on the exam.
(d) Construct a conditional distribution of immigration opinion by ethnicity. Ethnicity Opinion Non-Hispanic Whites Blacks Hispanics Good thing 0.597 0.542 0.742 Bad thing 0.345 0.370 0.167 Good and bad 0.029 0.049 0.061 No opinion 0.029 0.039 0.030 Total 1 1 1 (Round to three decimal places as needed.)
It's the seperated race votes divided by the race totals.
Determine the required value of the missing probability to make the distribution a discrete probability distribution. x P(x) 3 0.26 4 ? 5 0.45 6 0.12
P(4) = 0.17 (Type an integer or a decimal.)
An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $50 comma 000. If the economy grows at a moderate pace, the investment will result in a profit of $20 comma 000. However, if the economy goes into recession, the investment will result in a loss of $50 comma 000. You contact an economist who believes there is a 20% probability the economy will remain strong, a 60% probability the economy will grow at a moderate pace, and a 20% probability the economy will slip into recession. What is the expected profit from this investment?
The expected profit is $ 12,000. (Type an integer or a decimal.)
Find the probability P(Upper E Superscript c) if P(E)equals0.39.
The probability P(Upper E Superscript c) is 0.61. (Simplify your answer.)
A police officer randomly selected 583 police records of larceny thefts. The accompanying data represent the number of offenses for various types of larceny thefts. (a) Construct a probability model for type of larceny theft. (b) Are coin dash operated machine larcenies unusual? (c) Are larcenies from buildings unusual?
(a) Complete the table below. Type of Larceny Theft Probability Pocket picking 0.007 Purse snatching 0.009 Shoplifting 0.196 From motor vehicles 0.372 Motor vehicle accessories 0.148 Bicycles 0.084 From buildings 0.175 From coin-operated machines 0.010 (b) Choose the correct answer below. A. Yes, because P(coin dash operated machine)less than0.05. (c) Choose the correct answer below. A. No, because P(larcenies from buildings)greater than0.05.
A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the accompanying data. Complete parts (a) through (g) below.
(a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. Y = 0.177x + (12.768) (b) Interpret the slope and y-intercept, if appropriate. Interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. C. For every inch increase in height, the head circumference increases by 0.176 in., on average. Interpret the y-intercept, if appropriate. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. E. It is not appropriate to interpret the y-intercept. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Y = 17.18 in. (Round to two decimal places as needed.) Compute the residual based on the observed head circumference of the 25-inch-tall child in the table. Is the head circumference of this child above or below the value predicted by the regression model? The residual for this observation is -0.28, meaning that the head circumference of this child is below the value predicted by the regression model. (Round to two decimal places as needed.) (e) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (d). Choose the correct graph below. (b) check graphs better Notice that two children are 26.5 inches tall. One has a head circumference of 17.4 inches; the other has a head circumference of 17.6 inches. How can this be? B. For children with a height of 26.5 inches, head circumferences vary. (g) Would it be reasonable to use the least-squares regression line to predict the head circumference of a child who was 32 inches tall? Why? D. No - height is outside the scope of the model.
Suppose that a recent poll found that 62% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c).
(a) For 200 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor. The mean of X is 124. (Round to the nearest whole number as needed.) The standard deviation of X is 6.9. (Round to the nearest tenth as needed.) D. For every 200 adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor. (c) Would it be unusual if 125 of the 200 adults surveyed believe that the overall state of moral values is poor? Yes
In an effort to gauge how the country's population feels about the immigration, researchers surveyed adult citizens. One question asked was, "On the whole, do you think immigration is a good thing or a bad thing for this country today?" The results of the survey, by ethnicity, are given in the acompanying table. Complete parts (a) through (f).
(a) How many adult citizens were surveyed? 786 How many Hispanics were surveyed? 198 (b) Construct a relative frequency marginal distribution. Ethnicity Opinion Non-Hispanic Whites Blacks Hispanics Relative frequency marginal distribution Good thing 185 152 147 0.616 Bad thing 107 101 33 0.307 Good and bad 9 14 12 0.045 No opinion 9 11 6 0.033 Relative frequency marginal distribution 0.394 0.354 0.252 1 (Round to three decimal places as needed.) (c) What proportion of adult citizens feel that immigration is a good thing for this country? 0.616 (Round to three decimal places as needed.) (d) Construct a conditional distribution of immigration opinion by ethnicity. Ethnicity Opinion Non-Hispanic Whites Blacks Hispanics Good thing 0.597 0.547 0.742 Bad thing 0.345 0.363 0.167 Good and bad 0.029 0.050 0.061 No opinion 0.029 0.040 0.030 Total 1 1 1 (Round to three decimal places as needed.) (f) Is ethnicity associated with opinion regarding immigration? If so, how? Choose the correct answer below. C. Yes, ethnicity is associated with opinion regarding immigration. Hispanics are more likely to feel that immigration is a good thing for the country and much less likely to feel it is a bad thing.
A book can be classified as either non dash fiction or fiction. Suppose that 94% of books are classified as fiction. (a) Two books are chosen at random. What is the probability that both books are fiction? (b) Seven books are chosen at random. What is the probability that all seven books are fiction? (c) What is the probability that at least one of seven randomly selected books is non dash fiction? Would it be unusual that at least one of seven randomly selected books is non dash fiction?
(a) Two books are chosen at random. What is the probability that both books are fiction? The probability is 0.8836. (Round to four decimal places as needed.) (b) Seven books are chosen at random. What is the probability that all seven books are fiction? The probability is 0.6485. (Round to four decimal places as needed.) (c) What is the probability that at least one of seven randomly selected books is non dash fiction? The probability is 0.3515. (Round to four decimal places as needed.) Would it be unusual that at least one of seven randomly selected books is non dash fiction? It would not be unusual that at least one of seven randomly selected books is non dash fiction.
Is the width of a tornado related to the amount of distance for which the tornado is on the ground? The accompanying data represent the width (yards) and length (miles) of tornadoes in a particular region for one calendar year. Complete parts (a) through (n) below.
(a) What is the explanatory variable? Width (b) Explain why this data should be analyzed as bivariate quantitative data. For each tornado, two quantitative variables are measured: width and length. There is a positive relationship between the width and length of a tornado. (d) Determine the correlation coefficient between width and length. requals 0.859 (Round to three decimal places as needed.) (e) Is there a linear relation between a tornado's width and its length on the ground? Yes (f) Find the least squares regression line. ModifyingAbove y with caretequals 0.010xplusleft parenthesis nothing right parenthesis (g) Predict the length of a tornado whose width is 300 yards. 3.3 miles (h) Was the tornado whose width is 790 yards and length was 3.6 miles on the ground longer than would be expected? No, the predicted length of a tornado with width 790 yards is 8.2 miles, so 3.6 miles is less than expected. (Round to one decimal place as needed.) (i) Interpret the slope. For each yard increase in tornado width, the tornado length increases by 0.010, on average. (Round to three decimal places as needed.) (j) Explain why it does not make sense to interpret the intercept. Select the correct choice below and, if necessary, fill in any answer box to complete your choice. A. The width of the tornado cannot be 0 yards. (Type an integer or a decimal. Do not round.) (k) What proportion of the variability in tornado length is explained by the width of the tornado? 73.8% (Round to one decimal place as needed.) The residual plot suggests that the two variables are likely linearly related. There exists at least one outlier. (n) A major tornado was 4562 yards wide that had a length of 16.9 miles. Is this an influential tornado? Explain. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. C. Yeslong dashwith the point (4562,16.9) included in the regression, the slope changes to 0.006 and the intercept changes to 1.449. (Round to three decimal places as needed.)
Researchers initiated a long-term study of the population of American black bears. One aspect of the study was to develop a model that could be used to predict a bear's weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The accompanying data represent the lengths and weights of 12 American black bears. Complete parts (a) through (d) below.
(a) Which variable is the explanatory variable based on the goals of the research? C. The length of the bear. Draw a scatter diagram of the data. Choose the correct graph below. B. Check graphs. Determine the linear correlation coefficient between weight and length. The linear correlation coefficient between weight and length is r = 0.715. Does a linear relation exist between the weight of the bear and the length? Because the correlation coefficient is positive and the absolute value of the correlation coefficient, 0.715, is greater than the critical value for this data set, 0.576, a positive linear relation exists between the weight of the bear and the length.
