Stats quizzes and some HW

Alex hypothesized​ that, on​ average, students study less than the recommended two hours per credit hour each week outside of class. Which of the following is the null hypothesis Alex will​ test?

H0: μx=2 hours per week per credit

It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each​ night, on average. The researcher randomly sampled 50 college students and calculated a sample mean of 7.9 hours per night. The researcher performed a hypothesis test. What is the null​ hypothesis?

H0: μx=8 hours per night

Alex hypothesized​ that, on​ average, students study less than the recommended two hours per credit hour each week outside of class. Which of the following is​ Alex's alternative​ hypothesis?

H1: μ<2 hours per week per credit

Identify the requirements for a discrete probability distribution.

The sum of the probabilities must equal one. Each probability must be between zero and one inclusive.

The graph of a normal curve is given. Use the graph to identify the value of μ and σ.

The value of μ is 100. The value of σ is 15.

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n=50​, p=0.97​, x= 48 P(48)=___

P(48)= 0.2555

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n=50​, p=0.98​, x=48

P(48)=0.1858

Suppose that E and F are two events and that P(E)=0.5 and P(F|E)=0.3. What is P(E and F)​?

P(E and F)= 0.15

Find the probability of the indicated event if ​P(E)=0.30 and ​P(F)=0.45. Find​ P(E or​ F) if​ P(E and ​F)=0.10.

P(E or F)= 0.65

If ​P(E)=0.40​, ​P(E or​F)=0.65​, and​ P(E and F)=0.10​, find​ P(F).

P(F)= 0.35

Suppose a life insurance company sells a ​$210,000 ​one-year term life insurance policy to a 24​-year-old female for ​$170. The probability that the female survives the year is 0.999649. Compute and interpret the expected value of this policy to the insurance company. The expected value is $___. Which of the following interpretation of the expected value is​ correct?

$69.29 The insurance company expects to make an average profit of ​$96.29 on every 24-year-old female it insures for 1 year.

A test to determine whether a certain antibody is present is 99.8​% effective. This means that the test will accurately come back negative if the antibody is not present​ (in the test​ subject) 99.8​% of the time. The probability of a test coming back positive when the antibody is not present​ (a false​ positive) is 0.002. Suppose the test is given to six randomly selected people who do not have the antibody. ​(a) What is the probability that the test comes back negative for all six ​people? ​(b) What is the probability that the test comes back positive for at least one of the six ​people?

(a) P(all 6 tests are negative)= 0.9881 (b) P(at least one positive)=0.0119

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=0.946​, (b) r=1​, (c)= 0.787

(a) Scatter diagram II. ​(b) Scatter diagram III. ​(c) Scatter diagram I.

According to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe​ people's habits as they sneeze. ​(​a) What is the probability that among 16 randomly observed individuals exactly 6 do not cover their mouth when​ sneezing? ​(​b) What is the probability that among 16 randomly observed individuals fewer than 4 do not cover their mouth when​ sneezing? ​(​c) Would you be surprised​ if, after observing 16 ​individuals, fewer than half covered their mouth when​ sneezing? Why?

(​a) The probability that exactly 6 individuals do not cover their mouth is 0.1299. ​(​b) The probability that fewer than 4 individuals do not cover their mouth is 0.3460. ​(​c) Fewer than half of 16 individuals covering their mouth would be surprising because the probability of observing fewer than half covering their mouth when sneezing is 0.0118​, which is an unusual event.

If r=​_______, then a perfect negative linear relation exists between the two quantitative variables.

-1

A random sample of 1005 adults in a certain large country was asked​ "Do you pretty much think televisions are a necessity or a luxury you could do​ without?" Of the 1005 adults​ surveyed, 511 indicated that televisions are a luxury they could do without. Complete parts​ (a) through​ (e) below.

...

A company advertises a mean lifespan of 1000 hours for a particular type of light bulb. If you were in charge of quality control at the​ factory, would you prefer that the standard deviation of the lifespans for the light bulbs be 5 hours or 50​ hours? Why?

5 hours would be preferable since a smaller standard deviation indicates more consistency.

It is hypothesized that​ 50% of Americans attend church regularly. Which of the following would be an example of making a Type I​ Error?

A study was conducted that had evidence to reject the null hypothesis. In​ reality, half of Americans actually do attend church regularly.

Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is​ linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. A. Do the two variables have a linear​ relationship? B. If the relationship is linear do the variables have a positive or negative​ association?

A. The data points do not have a linear relationship because they do not lie mainly in a straight line. B. The relationship is not linear.

Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is​ linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. A.Do the two variables have a linear​ relationship? B. Do the two variables have a positive or a negative​ association?

A. The data points have a linear relationship because they lie mainly in a straight line. B.The two variables have a negative association.

The following data represent the miles per gallon for a particular make and model car for six randomly selected vehicles. Compute the​ mean, median, and mode miles per gallon. 35.7​, 38.8​, 26.1​, 30.5​, 27.9​, 22.2 (a)Compute the mean miles per gallon. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. (b)Compute the median miles per gallon. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. (c)Compute the mode miles per gallon. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. The mean mileage per gallon is 30.20. B. The median mileage per gallon is 29.20. C. The mode does not exist.

Suppose that a recent poll found that 55​% of adults believe that the overall state of moral values is poor. Complete parts​ (a) through​ (c). ​(a) For 300 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. ​(b) Interpret the mean. Choose the correct answer below. ​(c) Would it be unusual if 165 of the 300 adults surveyed believe that the overall state of moral values is​ poor?

A. The mean of X is 165.​ The standard deviation of X is 8.6. B. For every 300 ​adults, the mean is the number of them that would be expected to believe that the overall state of moral values is poor. C. No.

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean μ=291 days and standard deviation σ=22 days. ​(a) What is the probability that a randomly selected pregnancy lasts less than 284 ​days? ​(b) Suppose a random sample of 18 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.

A. The probability that a randomly selected pregnancy lasts less than 284 days is approximately 0.3752. If 100 pregnant individuals were selected independently from this​ population, we would expect 3838 pregnancies to last less than 284 days.

A data set is given below. ​(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. ​(b) Given that x=3.6667​, sx=2.3381​, y=4.1333​, sy=1.7907​, and r=−0.9474​, determine the​ least-squares regression line. ​(c) Graph the​ least-squares regression line on the scatter diagram drawn in part​ (a). x: 1 1 3 5 6 6 y: 5.2 6.5 5.4 3.0 2.2 ​(a) Choose the correct graph below. There appears to be ____relationship (b) y=__x=__ (c)​ Choose the correct graph below.

A. a. a linear, negative B. (y-hat) y= -0.726x +6.794 C.

Suppose the birth weights of​ full-term babies are normally distributed with mean 3450 grams and standard deviation σ=475 grams. Complete parts​ (a) through​ (c) below. ​(a) Draw a normal curve with the parameters labeled. Choose the correct graph below. (b) Shade the region that represents the proportion of​ full-term babies who weigh more than 4400 grams. Choose the correct graph below. (c) Suppose the area under the normal curve to the right of X=4400 is 0.0228. Provide an interpretation of this result. Select the correct choice below and fill in the answer box to complete your choice.

A. d B. b C. The probability is 0.0228 that the birth weight of a randomly chosen​ full-term baby in this population is more than 4400 grams.

Find the sample variance and standard deviation. 6​, 45​, 16​, 50​, 34​, 27​, 31​, 29​, 35​, 29 (a)Choose the correct answer below. Fill in the answer box to complete your choice. (b)Choose the correct answer below. Fill in the answer box to complete your choice.

A. s^2=161. 07 B. s=12.7

The following data represent the number of games played in each series of an annual tournament from 1928 to 2002. Complete parts​ (a) through​ (d) below. x​ (games played) 4 5 6 7 Frequency 16 15 19 24 ​(a) Construct a discrete probability distribution for the random variable x. ​(b) Graph the discrete probability distribution. Choose the correct graph below. ​(c) Compute and interpret the mean of the random variable x. Interpret the mean of the random variable x. ​(d) Compute the standard deviation of the random variable x.

A. x​ (games played) ​P(x) 4 0.2162 5 0.2027 6 0.2568 7 0.3243 B. d C.μx=5.6892 The​ series, if played many​ times, would be expected to last about 5.7 ​games, on average. D. σx=1.1 games

A simple random sample of size n=36 is obtained from a population with μ=89 and σ=24. ​(a) Describe the sampling distribution of x. ​(b) What is P x>95​? ​(c) What is P x≤81​? ​(d) What is P 84.4<x<95.4​?

A.The distribution is approximately normal. Find the mean and standard deviation of the sampling distribution of x. μx=89 σx=4 ​(b) P x>95=0.0668 ​ ​(c) P x≤81=0.0228 ​(d) P 84.4<x<95.4=0.8201

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. ​(b) Interpret the slope and​ y-intercept, if appropriate. First interpret the slope. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. Interpret the​ y-intercept, if appropriate. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. ​(d) 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? ​(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. ​(f) Notice that two children are 26.5 inches tall. One has a head circumference of 17.5 ​inches; the other has a head circumference of 17.7 inches. How can this​ be? ​(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?

A.y=0.158x+13.4 B.For every inch increase in​ height, the head circumference increases by 0.158 ​in., on average. It is not appropriate to interpret the​ y-intercept. C. y= 17.34 in D.The residual for this observation is −0.14​, meaning that the head circumference of this child is below the value predicted by the regression model. E. c F. For children with a height of 26.5 ​inches, head circumferences vary. G.No—this height is outside the scope of the model.

A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence assuming s=11.4 based on earlier​ studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size​ required? Level of​ Confidence, ​(1−α​)•​100% Area in Each​ Tail, α2 Critical​ Value, zα/2 ​90% 0.05 1.645 ​95% 0.025 1.96 ​99% 0.005term-0 2.575

A​ 99% confidence level requires 216 subjects. ​ A 95% confidence level requires 125 subjects. How does the decrease in confidence affect the sample size​ required? Decreasing the confidence level decreases the sample size needed.

A​ p-value is the probability​ _____________.

A​ p-value is the probability of observing the actual​ result, a sample​ mean, for​ example, or something more unusual just by chance if the null hypothesis is true.

The manufacturer of hardness testing equipment uses​ steel-ball indenters to penetrate metal that is being tested.​ However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of​ indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made.​ Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a​ 95% confidence interval to judge whether the two indenters result in different measurements. ​Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Steel ball 50 57 61 71 68 54 65 51 53 Diamond 52 55 63 74 69 55 68 51 56

Construct a​ 95% confidence interval to judge whether the two indenters result in different​ measurements, where the differences are computed as​ 'diamond minus steel​ ball'. The lower bound is 0.2. The upper bound is 2.7. State the appropriate conclusion. There is sufficient evidence to conclude that the two indenters produce different hardness readings.

A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms.

Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the α=0.05 level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers. State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms. H0​: μ1=μ2 H1​:μ1>μ2 Determine the​ P-value for this hypothesis test. ​P-value=0.488 State the appropriate conclusion. Do not reject H0. There is not significant evidence at the α=0.05 level of significance to conclude that carpeted rooms have more bacteria than uncarpeted rooms.

A freshman in college wanted to determine if the​ "Freshman 15" is true. That​ is, this student wanted to determine if freshmen in college gain more than 15 pounds during their freshman year. She randomly selected 50 freshmen during the first week of school at the beginning of the year and weighed them. During finals week of the last term of the​ year, she weighed the same 50 students. She recorded the weight change of each-a positive value indicated a weight gain while a negative value indicated a weight loss during the year. Based on her​ sample, a​ 95% confidence interval for the average weight change of freshmen during their freshman year is​ (8.9,12.1) lbs. What conclusion can be made based on this confidence​ interval?

It appears that the​ "Freshman 15" is not true. That​ is, it appears that freshman do not gain more than 15 pounds during their freshman​ year, on​ average, since the upper bound is less than 15.

​(d) Is it possible that a supermajority​ (more than​ 60%) of adults in the country believe that television is a luxury they could do​ without? Is it​ likely?

It is possible, but not likely that a supermajority of adults in the country believe that television is a luxury they could do without because the 95​% confidence interval does not contain 0.60.

Katy had two choices of routes to get her to work. She wanted to choose the route that would get her to work​ fastest, on average. To determine which route would get her to work​ faster, on​ average, she randomly selected 10 days and took Route 1 on those 10 days. Then she randomly selected a different 10 days and took Route 2 on those 10 days. She recorded the​ time, in​ minutes, it took her to get from her house to work on each of those 20 days. From her​ data, she constructed the​ 95% confidence interval for the difference in mean commuting times​ (Route 1−Route ​2) in minutes as ​(−​1,9). Based on this confidence​ interval, which of the following is NOT possible with​ 95% confidence?

It takes Katy 5 minutes longer to get to work using Route​ 2, on​ average, than Route 1.

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the 1246 males​ surveyed, 188 responded that they had at least one tattoo. Of the 1014 females​ surveyed, 134 responded that they had at least one tattoo. Construct a 95​% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

Let p1 represent the proportion of males with tattoos and p2 represent the proportion of females with tattoos. Find the 95​% confidence interval for p1−p2. The lower bound is −0.010. The upper bound is 0.048. Interpret the interval. There is 95​% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.

(e) Use the results of part​ (c) to construct a 95​% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.

Lower​ bound: 0.461,Upper​ bound: 0.522

Suppose the list below shows how many text messages Elyse sent each day for the last 10 days. If Elyse wants to know how many text messages she typically sends each​ day, which measure of central tendency better describes the typical number of text messages per​ day? 21 22 24 26 26 29 32 32 33 88

Median; The median of 27.5 is a better representative of the center since it is resistant to the one extreme value. The mean of 33.3 is not representative of the typical number of texts since only one number is larger than the mean.

In a national survey college students were​ asked, "How often do you wear a seat belt when riding in a car driven by someone​ else?" The response frequencies appear in the table to the right.​ (a) Construct a probability model for​ seat-belt use by a passenger.​ (b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone​ else? ​(a) Complete the table below. ​(b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone​ else?

Never 0.031 Rarely 0.066 Sometimes 0.122 Most of the time 0.219 Always 0.562 b. ​Yes, because ​P(never)<0.05.

A simple random sample of size n=35 is obtained from a population with μ=49 and σ=10. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally​ distributed? Why? What is the sampling distribution of x​?

No because the Central Limit Theorem states that regardless of the shape of the underlying​ population, the sampling distribution of x becomes approximately normal as the sample​ size, n, increases. The sampling distribution of x is normal or approximately normal with μx=49 and σx=1.690.

Determine whether the distribution is a discrete probability distribution. x 10 20 30 40 50 P(x) 0.25 0.25 0.25 0.25 0.25 Is the distribution a discrete probability​ distribution?

No, ​because the sum of the probabilities is not equal to 1.

Is the following a probability​ model? What do we call the outcome ​"blue​"? Color Probability red 0.15 green 0.3 blue 0 brown 0.2 yellow 0.1 orange 0.2

No​, because the probabilities do not sum to 1. Impossible event

Determine whether the distribution is a discrete probability distribution. x 0 100 200 300 400 P(x) 0.5 0.5 0.5 0.5 0.5 Is the distribution a discrete probability​ distribution?

No​, because the sum of the probabilities is not equal to 1.

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n=10​, p=0.3​, x=2 P(2)=___

P(2)= 0.2335

A​ one-sample test is to be performed. Researchers are wondering if the normality condition is met. The normal probability plot below was constructed based on data collected on GPAs from a random sample of college students. Based on the normal probability​ plot, which of the following statements is​ correct?

Since the sample data appear to be normally distributed and since a random sample was​ taken, it can be said that GPAs of all college students follow a normal distribution.

It has long been stated that the mean temperature of humans is 98.6°F. ​However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°F. They measured the temperatures of 61 healthy adults 1 to 4 times daily for 3​ days, obtaining 275 measurements. The sample data resulted in a sample mean of 98.3°F and a sample standard deviation of 1°F. Use the​ P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the α=0.01 level of significance.

State the hypotheses. H0​: μ = 98.6°F H1​: μ < 98.6°F Find the test statistic. t0=−4.97 The​ P-value is 0.000. What can be​ concluded? Reject H0 since the​ P-value is less than the significance level.

The mean finish time for a yearly amateur auto race was 185.93 minutes with a standard deviation of 0.397 minute. The winning​ car, driven by Ted​, finished in 184.79 minutes. The previous​ year's race had a mean finishing time of 110.1 with a standard deviation of 0.112 minute. The winning car that​ year, driven by Nina​, finished in 109.83 minutes. Find their respective​ z-scores. Who had the more convincing​ victory? Which driver had a more convincing​ victory?

Ted had a finish time with a​ z-score of negative −2.87. Nina had a finish time with a​ z-score of negative −2.41. Ted had a more convincing victory because of a lower​ z-score.

A study was conducted that resulted in the following relative frequency histogram. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.

The histogram is not bell-shaped, so a normal distribution could not be used for the variable.

The notation P(F E) means the probability of event ___ given event ___.

The notation P(F E) means the probability of event F given event E.

Complete the statement below. The points at x=​_______ and x=​_______ are the inflection points on the normal curve.

The points are x=μ−σ and x=μ+σ.

In a certain card​ game, the probability that a player is dealt a particular hand is 0.34. Explain what this probability means. If you play this card game 100​ times, will you be dealt this hand exactly 34 ​times? Why or why​ not?

The probability 0.34 means that approximately 34 out of every 100 dealt hands will be that particular hand.​ No, you will not be dealt this hand exactly 34 times since the probability refers to what is expected in the​ long-term, not​ short-term.

Suppose that events E and F are​ independent, ​P(E)=0.3​, and ​P(F)=0.6. What is the P(E and F)​?

The probability P(E and F) is 0.18.

Find the probability ​P(E^c​) if ​P(E)=0.21.

The probability P(E^c​) is 0.79

What is the probability of obtaining four tails in a row when flipping a​ coin? Interpret this probability. The probability of obtaining four tails in a row when flipping a coin is____ Consider the event of a coin being flipped four times. If that event is repeated ten thousand different​ times, it is expected that the event would result in four tails about ___​time(s).

The probability of obtaining four tails in a row when flipping a coin is 0.0625. Consider the event of a coin being flipped four times. If that event is repeated ten thousand different​ times, it is expected that the event would result in four tails about 625 ​time(s).

Suppose you just received a shipment of nine televisions. Two of the televisions are defective. If two televisions are randomly​ selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not​ work?

The probability that both televisions work is 0.200 The probability that at least one of the two televisions does not work is 0.800

Suppose you just received a shipment of nine televisions. Three of the televisions are defective. If two televisions are randomly​ selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not​ work?

The probability that both televisions work is 0.417. The probability that at least one of the two televisions does not work is 0.583.

A golf ball is selected at random from a golf bag. If the golf bag contains 9 type A​ balls, 8 type B​ balls, and 6 type C​ balls, find the probability that the golf ball is not a type A ball.

The probability that the golf ball is not a type A ball is 0.609.

Is the average body temperature of humans really 98.6°​F? After sampling​ 15,600 healthy people from around the​ country, researchers found a sample mean of 98.5°F. The​ p-value was 0.0001. Which of the following is​ true?

The results are​ "statistically significant" because the sample size was quite large and the​ p-value was quite small.

​(b) Verify that the requirements for constructing a confidence interval about p are satisfied.

The sample is stated to be a simple random​ sample, the value of np(1-p) is 251.186, which is greater than or equal to 10, and the sample size can be assumed to be less than or equal to​ 5% of the population size.

Alex hypothesized​ that, on​ average, students study less than the recommended two hours per credit hour each week outside of class. Alex performed a hypothesis test and obtained a​ p-value of 0.01. Assuming all conditions are​ met, which of the following is the most appropriate​ conclusion?

There is evidence to indicate students study less than the recommended two hours per credit hour each​ week, on average.

Elmo likes music. He wondered if listening to music while studying will improve scores on an exam. Fifty students who were to take the midterm in a week agreed to be part of a study. Half were randomly assigned to listen to classical music while studying for the exam. The other half were told not to listen to any music while studying for the exam. A hypothesis test is to be performed to determine if the average score of those listening to music while studying for the exam was higher than for those who did not listen to any music while studying for the exam. Which of the following is the correct null​ hypothesis?

There is no difference in the mean midterm scores between those who listen to classical music while studying and those who​ don't listen to music while studying.

It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the recommended number of hours of sleep each​ night, on average. The researcher randomly sampled 20 college students and obtained a​ p-value of 0.10. Suppose the researcher sampled more college students and that the sample mean and sample standard deviation stayed the same. Would the​ p-value be​ lower, be​ higher, or stay the​ same?

The​ p-value would be lower compared to the​ p-value from the sample with 20 college students.

A study was conducted based on a sample size of 30 individuals. The​ p-value was 0.10. Suppose a researcher conducted another study by taking a random sample of 50 individuals from the same population. Suppose they obtained the same sample mean as in the first study with a sample size of 30.​ (Also assume the population standard deviation is the same for both​ studies.) Which of the following is​ true?

The​ p-value would be smaller for the second study.

Is the statement below true or​ false? The​ least-squares regression line always travels through the point x,y(with the lines on top).

True The statement is true. The​ least-squares regression line is y=b1x+b0 where b0=y−b1x. That means that by​ definition, the predicted value for x is b1x+y−b1x which simplifies back to y.

In​ randomized, double-blind clinical trials of a new​ vaccine, infants were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second​ dose, 107 of 741 subjects in the experimental group​ (group 1) experienced drowsiness as a side effect. After the second​ dose, 64 of 622 of the subjects in the control group​ (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.10 level of​ significance?

Verify the model requirements. Select all that apply. A. The samples are independent. C. n1p11−p1≥10 and n2p21−p2≥10 D. The sample size is less than​ 5% of the population size for each sample. Determine the null and alternative hypotheses. H0​:p1=p2 H1​:p1>p2 Find the test statistic for this hypothesis test. 2.30 Determine the​ P-value for this hypothesis test. 0.011 Interpret the​ P-value. If the population proportions are equal, one would expect a sample difference proportion greater than greater than the one observed in about 11 out of 1000 repetitions of this experiment. State the conclusion for this hypothesis test. Reject H0. There is sufficient evidence to conclude that a higher proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.10 level of significance.

(c) Construct and interpret a 95​% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without. Select the correct choice below and fill in any answer boxes within your choice.

We are 95​% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.478 and 0.539.

The given data represent the total compensation for 10 randomly selected CEOs and their​ company's stock performance in 2009. Analysis of this data reveals a correlation coefficient of r=−0.2130. What would be the predicted stock return for a company whose CEO made​ $15 million? What would be the predicted stock return for a company whose CEO made​ $25 million? What would be the predicted stock return for a company whose CEO made​ $15 million?

What would be the predicted stock return for a company whose CEO made​ $15 million? 17.3% What would be the predicted stock return for a company whose CEO made​ $25 million? 17.3%

Is the following a probability​ model? What do we call the outcome ​"green​"? Is the table above an example of a probability​ model? What do we call the outcome ​"green​"?

Yes, because the probabilities sum to 1 and they are all greater than or equal to 0 and less than or equal to 1. Impossible event.

The relative frequency histogram represents the length of phone calls on​ George's cell phone during the month of September. Determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.

Yes​, because the histogram has the shape of a normal curve.

Rejecting the null hypothesis when the null hypothesis is true is called​ _____________.

a Type I Error

What is the probability of an event that is​ impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is​ impossible? A. What is the probability of an event that is​ impossible? B. Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is​ impossible?

a. 0 b. No.

The standard deviation of the sampling distribution of x​, denoted σx​, is called the​ _____ _____ of the​ _____.

standard, error, mean

Determine whether the events E and F are independent or dependent. Justify your answer. ​(a) ​E: A person having an at-fault accident. ​F: The same person being prone to road rage. (b) ​E: A randomly selected person finding cheese revolting. ​F: A different randomly selected person finding cheese delicious. (c) ​E: The consumer demand for synthetic diamonds. ​F: The amount of research funding for diamond synthesis.

a. E and F are dependent because being prone to road rage can affect the probability of a person having an at-fault accident. b. E cannot affect F and vice versa because the people were randomly​ selected, so the events are independent. c. The consumer demand for synthetic diamonds could affect the amount of research funding for diamond synthesis​, so E and F are dependent.

A university conducted a survey of 362 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Complete parts​ (a) through​ (d) below. Fresh Soph Junior Senior Total Satisfied 54 46 68 55 223 Neutral 29 17 11 13 70 Not satisfied 18 15 14 22 69 Total 101 78 93 90 362 ​(a) If a survey participant is selected at​ random, what is the probability that he or she is satisfied with student​ government? ​(b) If a survey participant is selected at​ random, what is the probability that he or she is a​ junior? ​(c) If a survey participant is selected at​ random, what is the probability that he or she is satisfied and a​ junior? ​(d) If a survey participant is selected at​ random, what is the probability that he or she is satisfied or a​ junior?

a. P(satisfied)= 0.616 b. P(junior)= 0.257 c. P(satisfied and junior)= 0.188 d. P(satisfied or junior)= 0.685

In a recent​ poll, a random sample of adults in some country​ (18 years and​ older) was​ asked, "When you see an ad emphasizing that a product is​ "Made in our​ country," are you more likely to buy​ it, less likely to buy​ it, or neither more nor less likely to buy​ it?" The results of the​ survey, by age​ group, are presented in the following contingency table. Complete parts​ (a) through​ (c). Purchase likelihood 18-34 35-44 45-54 55+ Total More likely 224 346 388 409 1367 Less likely 20 6 29 19 74 Neither more nor less likely 281 205 158 145 789 Total 525 557 575 573 2230 ​(a) What is the probability that a randomly selected individual is 45 to 54 years of​ age, given the individual is more likely to buy a product emphasized as​ "Made in our​ country"? (b) What is the probability that a randomly selected individual is more likely to buy a product emphasized as​ "Made in our​ country," given the individual is 45 to 54 years of​ age? ​(c) Are​ 18- to​ 34-year-olds more likely to buy a product emphasized as​ "Made in our​ country" than individuals in​ general?

a. The probability is approximately 0.284 b. The probability is approximately 0.675 c. No, less likely

In a recent​ poll, a random sample of adults in some country​ (18 years and​ older) was​ asked, "When you see an ad emphasizing that a product is​ "Made in our​ country," are you more likely to buy​ it, less likely to buy​ it, or neither more nor less likely to buy​ it?" The results of the​ survey, by age​ group, are presented in the following contingency table. Complete parts​ (a) through​ (c). Purchase likelihood 18-34 35-44 45-54 55+ Total More likely 206 333 352 408 1299 Less likely 30 10 25 16 81 Neith m/ l likely 289 216 151 103 759 Total 525 559 528 527 2139 ​(a) What is the probability that a randomly selected individual is 45 to 54 years of​ age, given the individual is less likely to buy a product emphasized as​ "Made in our​ country"? (b) What is the probability that a randomly selected individual is less likely to buy a product emphasized as​ "Made in our​ country," given the individual is 45 to 54 years of​ age? ​(c) Are​ 18- to​ 34-year-olds more likely to buy a product emphasized as​ "Made in our​ country" than individuals in​ general?

a. The probability is approximately 0.309 b. The probability is approximately 0.047 c. No, less likely

The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=−0.981. The​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=−0.0069x+44.6554. Complete parts ​(a) and ​(b) below. ​(a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per​ gallon? ​(b) Interpret the coefficient of determination.

a. The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is 96.2 % (r=-0.981, r^2=0.962) b. 96.2% of the variance in gas mileage is explained by the linear model.

An engineer wants to determine how the weight of a​ car, x, affects gas​ mileage, y. The following data represent the weights of various cars and their miles per gallon. Car A B C D E Weight​ (lbs), x 2635 3045 3375 3770 4135 Miles p Gallon, y 27.1 26.7 25 24.7 19.5 ​(a) Find the​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. ​(b) Interpret the slope and​ intercept, if appropriate. Choose the best interpretation for the slope. Choose the best interpretation for the​ y-intercept. ​(c) Predict the miles per gallon of car D and compute the residual. Is the miles per gallon of this car above average or below average for cars of this​ weight? Is the value above or below​ average? ​(d) Draw the​ least-squares regression line on the scatter diagram of the data and label the residual. Which of the following represents the data with the residual shown in​ red?

a. Write the equation for the​ least-squares regression line. y=-0.00459x + 40.2 b.The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight. It is not appropriate to interpret the​ y-intercept because it does not make sense to talk about a car that weighs 0 pounds. c. The predicted value is 22.86 miles per gallon. The residual is 1.84 miles per gallon. It is above average. d. b

Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X>40) Which of the following normal curves corresponds to P(X>40)​?

b. P(X>40)= 0.9234

A​ __________ random variable has either a finite or countable number of values.

discrete

Two events E and F are​ ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.

independent

The following data represent the number of games played in each series of an annual tournament from 1928 to 2005. Complete parts​ (a) through​ (d) below. x​ (games played) 4 5 6 7 Frequency 16 13 17 31 ​(a) Construct a discrete probability distribution for the random variable x. ​(b) Graph the discrete probability distribution. Choose the correct graph below. ​(c) Compute and interpret the mean of the random variable x. Interpret the mean of the random variable x. ​(d) Compute the standard deviation of the random variable x.

​(a) Construct a discrete probability distribution for the random variable x. x​ (games played) ​P(x) 4 0.2078 5 0.1688 6 0.2208 7 0.4026 ​(b) d ​(c) μx=5.8182 games The​ series, if played many​ times, would be expected to last about 5.8 ​games, on average. ​(d) σx=1.21.2 games

According to an​ airline, flights on a certain route are on time 80​% of the time. Suppose 20 flights are randomly selected and the number of​ on-time flights is recorded. ​(a) Explain why this is a binomial experiment. ​(b) Find and interpret the probability that exactly 13 flights are on time. ​(c) Find and interpret the probability that fewer than 13 flights are on time. ​(d) Find and interpret the probability that at least 13 flights are on time. ​(e) Find and interpret the probability that between 11 and 13 ​flights, inclusive, are on time.

​(a) Identify the statements that explain why this is a binomial experiment. Select all that apply. -The experiment is performed a fixed number of times. -The probability of success is the same for each trial of the experiment. Your answer is correct. -There are two mutually exclusive​ outcomes, success or failure. -The trials are independent. ​(b) The probability that exactly 13 flights are on time is 0.0545. In 100 trials of this​ experiment, it is expected about 5 to result in exactly 13 flights being on time. (c) The probability that fewer than 13 flights are on time is 0.0321. In 100 trials of this​ experiment, it is expected about 3 to result in exactly 13 flights being on time. ​(d) The probability that at least 13 flights are on time is 0.9679. In 100 trials of this​ experiment, it is expected about 97 to result in exactly 13 flights being on time. ​(e) The probability that between 11 and 13 ​flights, inclusive, are on time is 0.0841. In 100 trials of this​ experiment, it is expected about 8 to result in between 11 and 13 ​flights, inclusive, being on time.

​(a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.

​(a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without. p=0.508 (p= 511/1005)

The data in the following table show the association between cigar smoking and death from cancer for 140,117 men.​ Note: current cigar smoker means cigar smoker at time of death. Died from Cancer Did Not Die Cancer Never scs 935 123,589 Former scs 72 9,025 Current scs 192 6,304 Click the icon to view the table. (a) If an individual is randomly selected from this​ study, what is the probability that he died from​ cancer? (b) If an individual is randomly selected from this​ study, what is the probability that he was a current cigar​ smoker? (c) If an individual is randomly selected from this​ study, what is the probability that he died from cancer and was a current cigar​ smoker? (d) If an individual is randomly selected from this​ study, what is the probability that he died from cancer or was a current cigar​ smoker?

​(a) P(died from ​cancer)=0.009 ​(b) P(current cigar smoker)=0.046 ​(c) P(died from cancer and current cigar ​smoker)= 0.001 ​(d) P(died from cancer or current cigar ​smoker)= 0054

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=−0.810​, (b) r=−1​, (c) r=−0.049

​(a) Scatter diagram II. ​(b) Scatter diagram I. ​(c) Scatter diagram III.

Match the coefficient of determination to the scatter diagram. The scales on the​ x-axis and​ y-axis are the same for each scatter diagram. (a) R2=0.27​, (b) R2=0.90​, (c) R2=1

​(a) Scatter diagram III. ​(b) Scatter diagram I. ​(c) Scatter diagram II.

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for a random sample of 1037 people age 15 or​ older, the mean amount of time spent eating or drinking per day is 1.52 hours with a standard deviation of 0.58 hour. Complete parts ​(a) through ​(d) below. ​(a) A histogram of time spent eating and drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day. ​(b) There are more than 200 million people nationally age 15 or older. Explain why​ this, along with the fact that the data were obtained using a random​ sample, satisfies the requirements for constructing a confidence interval. (c) Determine and interpret a 95​% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day. (d) Could the interval be used to estimate the mean amount of time a​ 9-year-old spends eating and drinking each​ day? Explain.

​(a) Since the distribution of time spent eating and drinking each day is not normally distributed​ (skewed right), the sample must be large so that the distribution of the sample mean will be approximately normal. ​(b) The sample size is less than​ 5% of the population. (c)The nutritionist is 95​% confident that the mean amount of time spent eating or drinking per day is between 1.485 and 1.555 hours. ​(d) No; the interval is about people age 15 or older. The mean amount of time spent eating or drinking per day for​ 9-year-olds may differ.

A computer can be classified as either cutting-edge or ancient. Suppose that 81​% of computers are classified as ancient. ​(a) Two computers are chosen at random. What is the probability that both computers are ancient​? ​(b) Six computers are chosen at random. What is the probability that all six computers are ancient​? ​(c) What is the probability that at least one of six randomly selected computers is cutting-edge​? Would it be unusual that at least one of six randomly selected computers is cutting-edge​?

​(a) Two computers are chosen at random. What is the probability that both computers are ancient​? The probability is (0.81 x 0.81=)0.6561. (b) Six computers are chosen at random. What is the probability that all six computers are ancient​? The probability is nothing (0.81^6) 0.2824. (c) What is the probability that at least one of six randomly selected computers is cutting-edge​? The probability is (E^C=1-.2824) 0.7176 It would not be unusual that at least one of six randomly selected computers is cutting-edge.

According to an​ almanac, 80​% of adult smokers started smoking before turning 18 years old. ​(a) Compute the mean and standard deviation of the random variable​ X, the number of smokers who started before 18 in 400 trials of the probability experiment. ​(b) Interpret the mean. ​(c) Would it be unusual to observe 360 smokers who started smoking before turning 18 years old in a random sample of 400 adult​ smokers? Why?

​(a) μx=320 σx=88 ​(b) What is the correct interpretation of the​ mean? It is expected that in a random sample of 400 adult​ smokers, 320 will have started smoking before turning 18. ​(c) Would it be unusual to observe 360 smokers who started smoking before turning 18 years old in a random sample of 400 adult​ smokers? Yes​, because 360 is greater than μ+2σ.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. A tennis player who aces 10​% of her serves is asked to hit serves until she gets an ace. The number of serves attempted is recorded. Does the probability experiment represent a binomial​ experiment?

​No, because the experiment is not performed a fixed number of times.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. Five cards are selected from a standard​ 52-card deck without replacement. The number of nines selected is recorded.

​No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.

Determine if the following probability experiment represents a binomial experiment. A random sample of 30 professional athletes is​ obtained, and the individuals selected are asked to state their heights.

​No, this probability experiment does not represent a binomial experiment because the variable is​ continuous, and there are not two mutually exclusive outcomes.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An experimental drug is administered to 190 randomly selected​ individuals, with the number of individuals responding favorably recorded.

​Yes, because the experiment satisfies all the criteria for a binomial experiment.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An investor randomly purchases 7 stocks listed on a stock exchange.​ Historically, the probability that a stock listed on this exchange will increase in value over the course of a year is 49​%. The number of stocks that increase in value is recorded.

​Yes, because the experiment satisfies all the criteria for a binomial experiment.

Determine whether the distribution is a discrete probability distribution. x ​P(x) 0 0.34 1 0.07 2 0.19 3 0.24 4 0.16 Is the distribution a discrete probability​ distribution?

​Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and​ 1, inclusive.