Stats Final
What are the two requirements for a discrete probability distribution?
0<or=P(x)<or=1 sum of P(x)=1
What is a residual? What does it mean when a residual is positive?
A residual is the difference between an observed value of the response variable y and the predicted value of y. If it is positive, then the observed value is greater than the predicted value.
Suppose that E and F are two events and that P(E and F)=0.7 and P(E)=0.8. What is P(F|E)?
P(F|E)=.875. (E and F)/(E)
According to a recent study, 8.7% of high school dropouts are 16- to 17-year-olds. In addition, 5.8% of high school dropouts are white 16- to 17-year-olds. What is the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old?
The probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old, is 0.6667. you do. .058/.087
The expected frequencies in a chi-square test for independence are found using the formula below.
True. It is a simplification of multiplying the proportion of a row variable by the proportion of the column variable to find the proportion for a cell, then multiplying by the table total.
The following data represent the time between eruptions and the length of eruption for 9 randomly selected geyser eruptions. The coefficient of determination is 88.6%. Provide an interpretation of this value.
a)(same percent that's in the question), length of eruption
True or False: The population proportion and sample proportion always have the same value
false
Suppose a person claims that, "0.7% of all people in the nation always eat out." Is this a descriptive or inferential statement?
inferential
Determine the expected count for each outcome.
n*p
Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 77th percentile.
qnorm(.77,mean= ,sd= )
In a survey of 2055 adults in a certain country conducted during a period of economic uncertainty, 52% thought that wages paid to workers in industry were too low. The margin of error was 3 percentage points with 95% confidence. For parts (a) through (d) below, which represent a reasonable interpretation of the survey results? For those that are not reasonable, explain the flaw.
(a) We are 95%confident 52%of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low. -The interpretation is flawed. The interpretation provides no interval about the population proportion (b) We are 92%to 98%confident 52% of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low. -The interpretation is flawed. The interpretation indicates that the level of confidence is varying. (c) We are 95% confident that the interval from 0.49to 0.55contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low. -The interpretation is reasonable. (d)In 95%of samples of adults in the country during the period of economic uncertainty, the proportion who believed wages paid to workers in industry were too low is between 0.49and 0.55. -The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the otherintervals, which is not true.
In a survey conducted by the Gallup Organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5. Provide two recommendations for decreasing the margin of error of the interval.
-Increase the sample size. -Decrease the confidence level.
What are some solutions to nonresponse?
-offer rewards and incentives -attempt callbacks
Compute the critical value zα/2 that corresponds to a 91% level of confidence.
1-.91=.9/2=.045 qnorm(.045)= 1.70
Determine the original set of data.
10,11,14,21,24,24,27,29.......
Find the value of the combination
10C5=252
Construct a confidence interval for p1−p2 at the given level of confidence. x1=381, n1=531, x2=432, n2=559, 95% confidence
2 proportions 95% a/2 for intervals
Suppose Aaron is going to build a playlist that contains 5 songs. In how many ways can Aaron arrange the 5 songs on the playlist?
Aaron can arrange the 5 songs on the playlist in 120 different ways (5*4*3*2*1)
What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p?
E(X)=np
Suppose that two variables, X and Y, are negatively associated. Does this mean that above-average values of X will always be associated with below-average values of Y? Explain.
No, because association does not mean that every point fits the trend. The negative association only means that above-average values of X are generally associated with below-average values of Y.
Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. A soccer player who makes 10% of her free kicks is asked to kick free kicks until she misses. The number of free kicks attempted is recorded.
No, because the experiment is not performed a fixed number of times.
Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that there are exactly 4 defective parts in a shipment.
The area between 3.5 and 4.5
Suppose there are n independent trials of an experiment with k>3 mutually exclusive outcomes, where pi represents the probability of observing the ith outcome. What would be the formula of an expected count in this situation?
The expected counts for each possible outcome are given by Ei=npi.
An investment counselor calls with a hot stock tip. He believes that if the economy remainsstrong, the investment will result in a profit of $50,000. If the economy grows at a moderatepace, the investment will result in a profit of $10,000. However, if the economy goes intorecession, the investment will result in a loss of $50,000. You contact an economist who believes there is a 20% probability the economy will remain strong, a 70% probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. What is the expected profit from this investment?
The expected profit is quiz:$12000 or exam:$6000. strong+same-decline=expected. (50000*.2)+(10000*.7)-(50000*.1)= expected profit
As part of a college literature course, students must read three classic works of literature from the provided list. Write a short description of the processes that can be used to generate a simple random sample of three books. Obtain a simple random sample of size 3 from this list.
a) -List each book on a separate piece of paper, place them all in a hat, and pick three. Your answer is correct. -Number the books from 1 to 9 and use a random number generator to produce 3 different numbers from 1 to 9 that correspond to the books selected. b)use chart
Researchers wanted to determine if there was an association between the level of happiness of an individual and their risk of heart disease. The researchers studied 1756 people over the course of 11 years. During this 11-year period, they interviewed the individuals and asked questions about their daily lives and the hassles they face. In addition, hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews were videotaped and studied to assess the emotions of the individuals. The researchers also determined which individuals in the study experienced any type of heart disease over the 11-year period. After their analysis, the researchers concluded that the happy individuals were less likely to experience heart disease. Complete parts (a) through (c).
a) -cohort study -by observing them over a long period of time b) -whether or not heart disease was contracted -Is the variable of interest -level of happiness -affects the other variable c)The researchers may be concerned with confounding that occurs when the effects of two or more explanatory variables are not separated or when there are some explanatory variables that were not considered in a study, but that affect the value of the response variable.
Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the α=0.05 level of significance with 20 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the α=0.05 level of significance based on a sample size of n=15. (c) Determine the critical value(s) for a two-tailed test of a population mean at the α=0.10 level of significance based on a sample size of n=12.
a) +1.725 qt(.1,df=20,lower.tail=FASLE) b)-1.761 qt(.01,df=9,lower.tail=TRUE) c)+-1.796. qt(.05/2,df=9,lower.tail=TRUE) do on rstudio
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a queen or two. (b) Compute the probability of randomly selecting a queen or two or seven. (c) Compute the probability of randomly selecting a six or spade.
a) P(queen or two)=.154 b) P(queen or two or seven)=.231 c) P(six or spade)=.308 a) p(heart or a diamond)=.5 b) p(heart of diamond or spade)=.75 c)p(either or spade)=.308
In studies for a medication, 14 percent of patients gained weight as a side effect. Suppose 405 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that (a) exactly 57 patients will gain weight as a side effect. (b) no more than 57 patients will gain weight as a side effect. (c) at least 65 patients will gain weight as a side effect. What does this result suggest?
a) dbinom(#,size= ,prob= ) mean= np. sd= sqrt (n*p*(1-p)). b)pnorm(#,mean= ,sd= ,lower.tail= ). c) 1-pnorm(#, mean=, sd=). REMEMBER for the pnorm ones you have to do the .5 thing more, greater than
The least-squares regression equation is y=706.5x+14,922 where y is the median income and x is the percentage of 25 years and older with at least abachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7444. Complete parts(a) through (d)
a)##30%= put 30 in for x then get answer b)lower,# c)For every percent increase in adults having at least a bachelor's degree, the median income increases by $706.5(slope), on average. d)It does not make sense to interpret the y-intercept because an x-value of 0 is outside the scope of the model.
Suppose Ari wins 38% of all chess games. (a) What is the probability that Ari wins two chess games in a row? (b) What is the probability that Ari wins six chess games in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that Ari wins six chess games in a row, but does not win seven in a row.
a).1444 .38*.38 b).003 .38^6 c).0019 (.36^6)*(1-.38)
The graph of the discrete probability to the right represents the number of live births by a mother 40 to 44 years old who had a live birth in 2015. Complete parts (a) through (d) below.
a).155 *red dot b).208 *add 4 and 5 red dot c).11 *add 6,7 & 8 red dots d)3.0 mean = *1(.238)+2(.276)+3(.168)+4(.115).....add all up
Twelve jurors are randomly selected from a population of 4 million residents. Of these 4 million residents, it is known that 46% are of a minority race. Of the 12 jurorsselected, 2 are minorities. (a) What proportion of the jury described is from a minority race? (b) If 12 jurors are randomly selected from a population where 46% are minorities, what is the probability that 2 or fewer jurors will be minorities? (c) What might the lawyer of a defendant from this minority race argue?
a).17 (2/12) b).0363 pbinom(2,size=12,prob=.46) c)The number of minorities on the jury is unusually low, given the composition of the population from which it came.
Suppose Nate wins 25% of all staring contests. (a) What is the probability that Nate wins two staring contests in a row? (b) What is the probability that Nate wins six staring contests in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that Nate wins six staring contests in a row, but does not win seven in a row.
a).25*.25 (percent given) b).25^6 c)(.25^6)*.75
Suppose you just purchased a digital music player and have put 7 tracks on it. After listening to them you decide that you like 4 of the songs. With the random feature on your player, each of the 7 songs is played once in random order. Find the probability that among the first two songs played (a) You like both of them. Would this be unusual? (b) You like neither of them. (c) You like exactly one of them. (d) Redo (a)-(c) if a song can be replayed before all 7 songs are played.
a).286,no 4/7 * 3/6 b).143. 3/7 * 2/6 c).571. (4/7 + 3/6)*(3/7 +4/6)=4/7 d).326,(4/7 * 4/7).184(3/7 * 3/7), .489 (4/7*3/7 + 3/7*4/7).
The random-number generator on calculators randomly generates a number between 0 and 1. The random variableX, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.79 and 0.99? (c) What is the probability of generating a number greater than 0.92?
a)1-1 b).99-.79=.2 c)1-.92=.08
A salesperson obtained a systematic sample of size 30 from a list of 750 clients. To do so, he randomly selected a number from 1 to 25, obtaining the number 18. He included in the sample the 18th client on the list and every 25th client thereafter. List the numbers that correspond to the 30 clients selected.
a)18,43,743 use the k=equation from exam 1
Suppose Allan is going to build a playlist that contains 8 songs. In how many ways can Allan arrange the 8 songs on the playlist?
a)8*7*6*5*4*3*2*1= 40320
What does it mean when an observational study is retrospective? What does it mean when an observational study is prospective?
a)A retrospective study requires that individuals look back in time or require the researcher to look at existing records. b)A prospective study collects the data over time.
Describe the sampling distribution of p. Assume the size of the population is 30,000. n=600, p=.7
a)Approximately normal because n≤0.05N and np(1−p)≥10. b)mean phat=.7 (same as p) c)use formula: sdhat=.019 (8.2)
Suppose a simple random sample of size n=150 is obtained from a population whose size is N=10,000 and whose population proportion with a specified characteristic is p=.4
a)Approximately normal because n≤0.05N and np(1−p)≥10. mean= the p given sd= sqrt .4*.6/150 ,sd=sqrtp*q/n b)studio pnorm(#,mean= ,sd= ,lower.tail) c)studio. pnorm(#,mean= ,sd= ,lower.tail) p(.44) # for studio =.44. (8.2)
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of customers arriving at a bank between noon and 1:00 P.M.. (b) The distance a baseball travels in the air after being hit.
a)The random variable is discrete. The possible values are x=0, 1, 2,.... b)The random variable is continuous. The possible values are d>0
In a relative frequency distribution, what should the relative frequencies add up to?
a)The relative frequencies add up to 1
The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is unknown.However, records indicate that the mean time is 11.1 minutes, and the standard deviation is 3.6 minutes. Complete parts (a) through (c) below.
a)The sample size needs to be greater than 30. b)rstudio. exam:.008? 1)sd=sd/sqrtn 2)pnorm(#,mean= ,sd= ,lower.tail= ) c)rstudio changing the first number until you get just under 10%. exam:10.7? quiz=10.3 (8.1)
The acceptable level for insect filth in a certain food item is 5 insect fragments (larvae, eggs, body parts, and so on) per 10 grams. A simple random sample of 60 ten-gram portions of the food item is obtained and results in a sample mean of x=5.6 insect fragments per ten-gram portion. Complete parts (a) through (c) below.
a)The sampling distribution is approximately normal because the sample size is large enough. b)mean = mean given sd=sqrt5/sqrt60 sd=sd/sqrtn c)RStudio- pnorm(#,mean= ,sd= ,lower.tail= ) This result is unusual because its probability is small d)Since this result is unusual, it is reasonable to conclude that the population mean is higher than 5.
The data on the right relate to characteristics of high-definition televisions A through E. Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete.
a)The high-definition television setups A through E. b)Size ,screen type, and number of channels available c)size:continuous screen type:qualitative #channels:discrete
A study conducted by researchers was designed "to determine if application of duct tape is as effective as cryotherapy in the treatment of common warts." The researchers randomly divided 69 patients into two groups. The 35 patients in group 1 had their warts treated by applying duct tape. The 34 patients in group 2 had their warts treated by cryotherapy. Once the treatments werecomplete, it was determined that 63% of the patients in group 1 and 79% of the patients in group 2 had complete resolution of their warts. The researchers concluded that cryotherapy is significantly more effective in treating warts than duct tape. Complete parts (a) through (d) below.
a)To determine if duct tape is as effective as cryotherapy in the treatment of warts b)Population: All people who have warts Sample:The 69 patients with warts c)63%of patients in group 1 and 79%of patients in group 2 had resolution of their warts d)cryotherapy is significantly more effective than duct tape in treating warts.
The following data represent the number of games played in each series of an annual tournament from 1921 to 2003. Complete parts (a) through (d) below.
a)add up all frequencies. divide each by whole to get the chart numbers. part/whole b)graph c)hx mean= sum of (x*p(x)) -The series, if played many times, would be expected to last about 5.8 games, on average. d)sd-in notebook
According to a survey, the probability that a randomly selected worker primarily drives a motorcycle to work is 0.885. The probability that a randomly selected worker primarily takes public transportation to work is 0.039. Complete parts (a) through (d).
a)calculate (.885+.039) b)calculate (1-previous answer) c)calculate (1-.885) d)No. The probability a worker primarily drives, walks, or takes public transportation would be greater than 1.
A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. Complete parts (a) through (i).
a)chart b)chart c)highest d)lowest e)%,inferential f)The results might differ because there is always variability because the individuals in a survey may not exactly reflect the makeup of the population. g)chart h)chart i)chart
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)chart (part/whole), they should add up to 1 b)Yes, because P(never)<0.05
For the accompanying data set, (a) draw a scatter diagram of the data, (b) by hand, compute the correlation coefficient, and (c) determine whether there is a linear relation between x and y.
a)chart >plot b)r-value >cor(x,y) c)positive,(calculated r value^),greater,(rvalue from chart), a positive
Researchers wanted to determine if there was an association between the level of satisfaction of an individual and their risk of breast cancer. The researchers studied 1563 people over the course of 5 years. During this 5-year period, they interviewed the individuals and asked questions about their daily lives and the hassles they face. In addition, hypothetical scenarios were presented to determine how each individual would handle the situation. These interviews were videotaped and studied to assess the emotions of the individuals. The researchers also determined which individuals in the study experienced any type of breast cancer over the 5-year period. After their analysis, the researchers concluded that the satisfied individuals were less likely to experience breast cancer. Complete parts (a) through (c).
a)cohort study, by observing them over a long period of time b)whether or not breast cancer was contracted, is the variable of interest, level of satisfaction, affects the other variable
A traffic safety company publishes reports about motorcycle fatalities and helmet use. In the first accompanying datatable, the distribution shows the proportion of fatalities by location of injury for motorcycle accidents. The second data table shows the location of injury and fatalities for 2065 riders not wearing a helmet. Complete parts (a) and (b) below.
a)follows, not follows expected=n*p (n= all observedes added up, p=probability) so 2065*.57 then do that for all using same n rstudio notebook rejects,does not follow b)head injuries, more, less
Suppose the monthly charges for cell phone plans are normally distributed with mean μ=$56 and standard deviation σ=$16. (a) Draw a normal curve with the parameters labeled. (b) Shade the region that represents the proportion of plans that charge less than $40. (c) Suppose the area under the normal curve to the left of X=$40 is 0.1587. Provide an interpretation of this result
a)graph b)graph c)The probability is 0.1587(probability is given in the question) that a randomly selected cell phone plan in this population is less than $(dollar amount in (C)) per month.
The following data represent the level of health and the level of education for a random sample of 1483 residents. Complete parts (a) and (b) below
a)independent, dependent rstudio vector:not, HS,some,bachelor b)by level of education so (not excellent)/( not excellent+good+fair+poor)*do this for all boxes
A survey of 36 randomly selected students who dropped a course was conducted at a college. The following results were collected. Complete parts (a) through (c)
a)just count how many each are b)independent-dependent rstudio-chap12 vector:male vector:fem c) by gender so (male course)/(male course+personal+work) *do this for all boxes
The accompanying histogram represents the total tax collected by a federal tax collection service for fifty regions of varying sizes and populations in a certain country. Explain why the graph is misleading.
a)look at chart -It does not take into account the size and population of each region.
The data to the right represent the number of customers waiting for a table at 6:00 P.M. for 40 consecutive Saturdays at Bobak's Restaurant. Complete parts (a) through (h) below.
a)make histogram b)The distribution is symmetric because the left and right sides are approximately mirror images.
Complete parts (a) through (d) for the sampling distribution of the sample mean shown in the accompanying graph.
a)mean on graph b)sd from graph c)The shape of the population is approximately normal. d)The standard deviation of the population from which the sample was drawn is 40, sdx(B)*sqrtn(given in the question)=40 (answer) d)sd*sqrtn (8.1)
The linear correlation between violent crime rate and percentage of the population that has a cell phone is −0.918 for years since 1995. Do you believe that increasing the percentage of the population that has a cell phone will decrease the violent crime rate? What might be a lurking variable between percentage of the population with a cell phone and violent crime rate?
a)no b)the economy
Michael went to the driving range with his range finder and hit 75 golf balls with his pitching wedge and measured the distance each ball traveled (in yards). The accompanying table shows his data. Complete parts a and b below.
a)normally distribution graph b)Yes, because the histogram shape resembles a normal curve, and the area of each bar is roughly equal to the area under the normal curve for the same region
A researcher wanted to determine whether certain accidents were uniformly distributed over the days of the week. The data show the day of the week for n=292 randomly selected accidents. Is there reason to believe that the accidents occur with equal frequency with respect to the day of the week at the α=0.05 level of significance?
a)p1=p2=....p7=1/7-at least one proportion is different from the others expected=n/7 *same #for all n=add up all observed rstudio notebook
Researchers wish to know if there is a link between hypertension (high blood pressure) and consumption of sugar. Past studies have indicated that the consumption of fruits offsets the negative impact of sugar consumption. It is also known that there is quite a bit of person-to-person variability as far as the ability of the body to process and eliminate sugar. However, no method exists for identifying individuals who have a higher ability to process sugar. It is recommended that daily intake of sugar should not exceed 5800 milligrams (mg). The researchers want to keep the design simple, so they choose to conduct their study using a completely randomized design. Complete parts (a) through (c).
a)response: blood pressure b)3 factors:daily consumption of fruits, body's ability to process sugar, daily consumption of sugar c)blood pressure:not a factor daily consumption of sugar: can be controlled Daily consumption of fruits:can be controlled bodys ability to process sugar:cannot be controlled age:is not a factor gender:is not a factor If factor cannot be controlled?.....Experimental units should be randomly assigned to each treatment group
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 19 minutes and a standard deviation of 4 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does takelonger, the customer will receive the service for half-price. What percent of customers receive the service forhalf-price? (b) If the automotive center does not want to give the discount to more than 3% of its customers, how long should it make the guaranteed time limit?
a)rstudio - exam:40.13%? pnorm(20min,mean= ,sd= , lower.tail=FALSE) because you are looking for the upper half b)rstudio - exam: 27 min? ^use same as up there and change the first number(whole numbers)/min until the percent gets to be under 10
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=−0.969. The least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=−0.0070x+44.5280. Complete parts (a) and (b) below.
a)rstudio >cor(x,y)^2=decimal then put into percent b)(same as A)%, gas milage, explained
The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers. Complete parts (a) through (c) below.
a)rstudio mean of data= point estimate b)rstudio one can be % confident that mean travel tax ....... (9.2) c)the researcher could decrease the level of confidence
According to a survey, 65% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly selected, and the number cleared by arrest or exceptional means is recorded
a)rstudio pbinom(39.5,size= ,prob= ,lower.tail=TRUE)-pbinom(38.5,size= ,prob= ,lower.tail=TRUE) b)rstudio pbinom(38.5 ,size= ,prob= ,lower.tail=TRUE)-pbinom(35.5,size= ,prob= ,lower.tail=TRUE) c)Yes, it would be unusual because 19 is less than μ−2σ. CHECK cause it could be different *.5 thing to pbinom
A club wants to sponsor a panel discussion on the upcoming national election. The club wants four of its members to lead the panel discussion. Write a short description of the processes that can be used to generate your sample. Obtain a simple random sample of size 4 from the table.
a)simple random sample? -Number the names from 1 to 25 and use a random number table to produce 4 different two digit numbers corresponding to the names selected. Your answer is correct. -List each name on a separate piece of paper, place them all in a hat, and pick four. b)use table and know how that its 1-25
The data in the accompanying table represent the ages of the presidents of a country on their first days in office. Complete parts (a) and (b)
a)stem and leaf plot-(0-4),(5-9) b)bell shaped, maybe depending on stem and leaf plot
The data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.963. Judge whether a t-interval could be constructed using the data in the sample.
a)suggests, > corr co, does not show, could. OPPOSITE corr co from chart is greater than corr co in problem
The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 4008 employees at the company and wants to conduct a systematic sample of size 40.
a)use k equation b)also use k equation *Insert whole numbers
A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained if he wishes the estimate to be within five percentage points with 90% confidence, assuming that (a) he uses the estimates of 22.8% male and 19.1% female from a previous year? (b) he does not use any prior estimates?
a)use the n= formula using previous data e=.05 n=356 b)n formula not using previous data n=536 (11.1)
Suppose a surveyor wants to conduct a phone survey about a new movie. He plans to take a simple random sample. However, some people do not want to participate. Do you believe this can affect the ability of the surveyor to obtain accurate polling results? If so, how?
a)Yes, especially if the people who do not want to participate have a trait that is not accurately represented by the remaining people in the sample
The research group asked the following question of individuals who earned in excess of $100,000 per year and those who earned less than $100,000 per year: "Do you believe that it is morally wrong for unwed women to have children?" Of the 1,205 individuals who earned in excess of $100,000 per year, 710 said yes; of the 1,310 individuals who earned less than $100,000 per year, 690 said yes. Construct a 95% confidence interval to determine if there is a difference in the proportion of individuals who believe it is morally wrong for unwed women to have children.
a/2 two proportions rstudio for bounds conf inter does not include 0, sufficient, greater than CHECK because it could be different
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=9, p=0.6, x<or=3
calculate=The probability of x≤3 successes is . 0994 pbinom(3,size=9,prob=.6)
Male and female populations of tortoises under 80 years old are represented by age in the table below. Complete parts (a) through(d).
make that chart from chapter one to solve by hand
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.
mean:Rstudio median:rstudio mode:does not exist
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 111, and the sample standard deviation, s, is found to be 10. (a) Construct a 95% confidence interval about μ if the sample size, n, is 22. (b) Construct a 95% confidence interval about μ if the sample size, n, is 17. (c) Construct a 90% confidence interval about μ if the sample size, n, is 22. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normallydistributed?
one mean a)rstudio a/2 for intervals b)rstudio- As the sample size decreases, the margin of error increases OR As the sample size increases, the margin of error decreases. c) rstudio-As the level of confidence decreases, the size of the interval decreases. OR As the level of confidence increases, the size of the interval increases. d)No, the population needs to be normally distributed. (9.2)
A simple random sample of size n=40 is drawn from a population. The sample mean is found to be 106.1, and the sample standard deviation is found to be 24.5. Is the population mean greater than 100 at the α=0.10 level ofsignificance?
one mean use rstudio reject, less than, is , greater than 100(this one stays the same though no matter what). *CHECK because it could be opposite (10.4)
A certain vehicle emission inspection station advertises that the wait time for customers is less than 8 minutes. A local resident wants to test this claim and collects a random sample of 49 wait times for customers at the testing station. He finds that the sample mean is 7.46 minutes, with a standard deviation of 3.5 minutes. Does the sample evidence support the inspection station's claim? Use the α=0.005 level of significance to test the advertised claim that the wait time is less than 8 minutes.
one mean =,<. greater, do not reject, is not, does not support. (10.4)
A golf association requires that golf balls have a diameter that is 1.68 inches. To determine if golf balls conform to thestandard, a random sample of golf balls was selected. Their diameters are shown in the accompanying data table. Do the golf balls conform to the standards? Use the α=0.05 level of significance.
one mean -t.test = and not= rstudio if its .01 level of sig: t stat=.75 p-value=.469 not, not
A simple random sample of size n=40 is drawn from a population. The sample mean is found to be x=120.3 and the sample standard deviation is found to be s=13.4. Construct a 99% confidence interval for the population mean.
one mean 1-.99=.01/2 qt(.005,df= ,lower.tail=)(9.3)
A can of soda is labeled as containing 13 fluid ounces. The quality control manager wants to verify that the filling machine is neither over-filling nor under-filling the cans. Complete parts (a) through (d) below
one mean a)=,not=. b)reject=is c)type1,reject,null d).01,small type 1=reject then not reject type 2=not reject then reject (10.1)
The life expectancy of a male during the course of the past 100 years is approximately 27,732 days. Use the table to the right to conduct a test using α=0.05 to determine whether the evidence suggests that chief justices live longer than the general population of males. Suggest a reason why the conclusion drawn may be flawed.
one mean t.test =,> p-value=.000 reject, there is flawed: The sample is not obtained using simple random sampling or from a randomized experiment (10.3)
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. H0: p=0.8 versus H1: p>0.8 n=200; x=175; α=.1
one proportion 10.2
Several years ago, 50% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,055 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,055 surveyed, 452 indicated that they were satisfied. Construct a 99% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed
one proportion = vs not = -interval contains the proportion being tested= not reject, in sufficient -interval does not contain the proportion being tested=reject,sufficient. (10.2)
A random sample of 1027 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 1027 adults surveyed, 514 indicated that televisions are a luxury they could do without. Complete parts (a) through (e) below.
one proportion a)phat=x/n b)is stated to be, np(1-p),#,greater than or equal to, sample size, can be assumed to be, population size c)we are 95% confident, interval in rstudio a/2 d)possible but not likely, does not contain,(percent in question as decimal) e)1-same intervals as above (9.1)
In a survey of 1016 adults, a polling agency asked, "When you retire, do you think you will have enough money to live comfortably or not. Of the 1016 surveyed, 532 stated that they were worried about having enough money to live comfortably in retirement. Construct a 95% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement.
one proportion a/2 there is a 95%.... rstudio
A certain drug can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reflux. The manufacturer of the drug claims that more than 92% of patients taking the drug are healed within 8 weeks. In clinical trials, 217 of 232 patients suffering from acid reflux disease were healed after 8 weeks. Test themanufacturer's claim at the α=0.05 level of significance.
one proportion rstudio. (10.2)
In a survey of 1020 adults, a polling agency asked, "When you retire, do you think you will have enough money to live comfortably or not. Of the 1020 surveyed, 541 stated that they were worried about having enough money to live comfortably in retirement. Construct a 95% confidence interval for the proportion of adults who are worried about having enough money to live comfortably in retirement.
one proportion a/2 (9.3)
Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided. Lower bound=0.124, upper bound=0.326, n=
point estimate:(upper+lower)/2 margin or error: (upper - lower)/2 # of individuals: n*point-estimate (from first problem)
The number of adult Americans from a random sample of n adults who support a bill proposing to extend daylight savings time is a binomial random variable. Assume that its probability will be approximated using the normal distribution. Describe the area under the normal curve that will be computed in order to determine the probability that more than 408 Americans support the bill.
quiz: Right of x=408.5 exam:x=right of 318.5 exam:right of x=348.5. REMEMBER the .5 thing
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=15, p=0.7, x=12
quiz:P(12)=.1700 dbinom(12,size=15,prob=.7) Exam:P(4)=.2186 dbinom(4,size=15,prob=.3)
Suppose that events E and F are independent, P(E)=0.6, and P(F)=0.6. What is the P(E and F)?
the probability of p(e and f)=.36. .6*.6=.36
Is the statement below true or false? The least-squares regression line always travels through the point (x,y).
true
A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below.
two mean dependent t.test should be on chapter 11 question sheet on what to do =0,<0 two dependent means yes, because 0 is not contained in the box plot
Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be aprofessor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200 students in group 1 had a mean score of 26.7 with a standard deviation of 4.5, while the 200 students in group 2 had a mean score of 15.6 with a standard deviation of 3.5. Complete parts (a) and (b) below
two means A)rstudio for bounds -The researchers are 95%confident that the difference of the means is in the interval b)Since the 95% confidence interval does not contain zero, the results suggest that priming does have an effect on scores
Conduct a test at the α=0.05 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p1>p2. The sample data are x1=124, n1=253, x2=134, and n2=312.
two proportions
In 1940, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasionconsume, alcoholic beverages?" Of the 1100 adults surveyed, 440 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 374 indicated that they were total abstainers. Complete parts (a) and (b) below
two proportions a) proportions b)- the samples are independent, n1p1(1-p1)>=10 and n2p2(1-p2)>=10 rstudio equal, greater than the absolute value or,0
Use the following information to complete steps (a) through (d) below. A random sample of n1=110 individuals results in x1=40 successes. An independent sample of n2=150 individuals results in x2=60 successes. Does this represent sufficient evidence to conclude that p1<p2 at the α=0.10 level of significance?
two proportions in
A book claims that more hockey players are born in January through March than in October through December. The following data show the number of players selected in a draft of new players for a hockey league according to their birth month. Is there evidence to suggest that hockey players' birthdates are not uniformly distributed throughout theyear? Use the level of significance α=0.05
uniformly, not uniformly expected count= all the same number 169/4, use chap 12 notebook, no: p-value less than a
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.
use either t.test of other test, this should be on mean/ proportion questions sheet a/2 0 not included is sufficient evidence (11.2)
The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point?
use upper and lower fence formulas
For the histogram on the right determine whether the mean is greater than, less than, or approximately equal to the median. Justify your answer.
x>M IF because the histogram is skewed right.
Find the Z-scores that separate the middle 13% of the distribution from the area in the tails of the standard normal distribution.
z-score:-.16,.16 middle 13%. 1-.13=.87/2=.435=a area of .435= score of -.16 and .16 *have to use chart or qnorm(.435)
A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 30 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases? (a) 10% of all adult Americans support the changes (b) 15% of all adult Americans support the changes
(a) The researcher must ask 82 more American adults. (b) The researcher must ask 49 more American adults CALCULATIONS, use the n equals formula I think then do n- original (8.2)
Without doing any computation, decide which has a higher probability, assuming each sample is from a population that is normally distributed with μ=100 and σ=15. Explain your reasoning. (a) P(90≤x≤110) for a random sample of size n=10 (b) P(90≤x≤110) for a random sample of size n=20
P(90≤x≤110) for a random sample of size n=20 has a higher probability. As n increases, the standard deviation decreases.
The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the α=0.05 level of significance.
a) p1=p2=p3 H1: At least one of the proportions is different from the others. b)rstudio vector:fails vectors:successes. follow chap 12 on notebook
