stat final
Consider sampling heights from the population of all female college soccer players in the United States. Assume the mean height of female college soccer players in the United States is μ = 67 inches and the standard deviation is σ = 3.8 inches. Suppose we randomly sample 99 values from this population and compute the mean, then repeat this sampling process 5,000 times and record all the means we get. Which of the following is the best approximation for the standard deviation of the 5,000 sample means? 0.038 0.38 3.8
.38
In the article Foods, Fortificants, and Supplements: Where Do Americans Get Their Nutrients? researchers analyze the nutrient and vitamin intake from a random sample of 16,110 U.S. residents. Researchers compare the level of daily vitamin intake for vitamin A, vitamin B-6, vitamin B-12, vitamin C, vitamin D, vitamin E and calcium. Unless otherwise stated, all hypothesis tests in the study are conducted at the 5% significance level. To test the claim (at 5% significance) that the proportion of U.S. residents who consume recommended levels of vitamin A is higher among women than men, researchers set up the following hypotheses: In this hypothesis test which of the following errors is a Type I error?
Researchers conclude that a larger proportion of women consume the recommended daily intake of vitamin A when there is actually no difference between vitamin A consumption for women and men
According to the Pew Research Center, the proportion of the American population who use only a cellular telephone (no landline) is 37%. Jason claims that the proportion of young American adults who do not have a landline is greater than 37%. He conducts a survey with a sample of randomly selected young American adults and finds that 38% do not have landlines. If we set up our null and alternative hypotheses as follows: H0:p=0.37 Ha:p>0.37 and find that: "p-value"=0.418. Does this provide enough evidence to support Jason's claim? Use an α=0.05 level of significance. Choose the correct answer below.
Since the p-value > α, do not reject the null hypothesis.
Parking survey: For a class assignment, a group of statistics students set up a table near the student parking lot. They asked students who passed by to complete a quick survey about whether they support the building of a multi-level parking structure that would add 425 new spaces at the college. They used the information from the survey to calculate the 95% confidence interval: (0.53, 0.72). To which population does the confidence interval apply?
The results do not apply to any population because this was a convenience sample.
An interactive poll on the front page of the CNN website in October 2011 asked if readers would consider voting for Herman Cain, who at the time, was a Republican presidential candidate. A statistics student used the information from the poll to calculate the 95% confidence interval. He got (0.53,0.59). He also conducted a hypothesis test. He found very strong evidence that more than half of voters would consider voting for Herman Cain. To what population do these conclusions apply?
The results do not apply to any population because this was a voluntary response sample.
Based on the limited amount of available student parking spaces on the GSU campus, students are being encouraged to ride their bikes (when appropriate). The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 128 students surveyed 6 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.
The sample needs to be random but we don't know if it is. The actual count of bike riders is too small. n*^p is not greater than 10.
The administration at GSU wants to estimate the number of parking spaces they will need next year. They survey 80 students; 75 of the students in the sample drive to campus by themselves each day. Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus?
The sample needs to be random but we don't know if it is. n(1−^p) is not greater than 10.The actual count of those who do not drive to campus is too small.
Suppose the American National Elections Studies agency (ANES) wishes to conduct a survey. It plans to ask a yes/no question to determine if those surveyed plan to vote for a certain candidate. One proposal is to randomly select 400 people and another proposal is to randomly select 1600 people. Which of the following is true regarding the sample proportion ^p of "yes" responses?
The sample proportion from sample of 1,600 is more likely to be close to the true population proportion, p.
A student survey was conducted at a major university, and data were collected from a random sample of 750 undergraduate students. One variable that was recorded for each student was the student's answer to the question "With whom do you find it easiest to make friends? Opposite sex/same sex/no difference." These data would be best displayed using which of the following?
pie chart
A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years. Construct a 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years. Round your answer to three decimal places.
(0.163, 0.189)
When buying a home, the interest rate given on a loan typically depends on the applicant's credit score. The Fair Isaac Corporation (FICO) is a major producer of credit scores. The following table contains 10 randomly selected loan applicants along with their FICO scores and the interest rates that they were given when financing their homes. The linear correlation coefficient between FICO score and home loan interest rate is:
- 0.9819
Concert marketing: GSU's Rialto Center for the Performing Arts wanted to investigate why ticket sales for the upcoming season significantly decreased from last year's sales. The marketing staff collected data from a survey of community residents. Out of the 110 people surveyed, only 7 received the concert brochure in the mail. Which of the following is a reason that the marketing staff should not calculate a confidence interval for the proportion of all community residents who received the concert brochure by mail?
-The actual count of community residents who received the concert brochure by mail is too small. -The sample needs to be random, but we don't know if it is. -n^p is not greater than 10.
Let A and B be two independent events such that P(A) = 0.3 and P(B) = 0.5. What is P(A and B)?
.15 p(A)*p(B)
Suppose a basketball team had a season of games with the following characteristics: Of all the games, 60% were at-home games. Denote this by H (the remaining were awaygames). Of all the games, 25% were wins. Denote this by W (the remaining were losses). Of all the games, 20% were at-home wins. Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.)
.20/.60 0.33
Gardeners on the west coast of the United States are investigating the difference in survival rates of two flowering plants in drought climates. Plant A has a survival rate of 0.77 and plant B has a survival rate of 0.44. The standard error of the difference in proportions is 0.084. What is the margin of error for a 99% confidence interval? Use critical value z = 2.576. MOE =
.216 MOE = SE * Z
An automobile dealer gathered data concerning the age and the type of vehicle that was purchased from a random sample of the people that bought vehicles from them in the past year. The data is contained in the table below. 20-39 years 40-59 years 60 years and older Total Truck 25 15 10 50 Car 10 20 10 40 SUV 12 17 35 64 Total 47 52 55 154 Suppose a buyer is selected at random from this group, what is the probability that the buyer is in the age group 40 - 59 and purchased an SUV? (The responses below are rounded to 4 decimals.)
0.1104
Dogs are inbred for such desirable characteristics as blue eye color, but an unfortunate by-product of such inbreeding can be the emergence of characteristics such as deafness. A 1992 study of Dalmatians (by Strain and others, as reported in The Dalmatians Dilemma) found the following: (i) 31% of all Dalmatians have blue eyes. (ii) 38% of all Dalmatians are deaf. (iii) If a Dalmatian has blue eyes, there is a 42% chance that it is deaf. What is the probability that a randomly chosen Dalmatian is blue-eyed and deaf?
0.31 * 0.42 = 0.1302
The score of golfers for a particular course follows a normal distribution that has a mean of 73 and a standard deviation of 3. Suppose a golfer played the course today. Find the probability that her score is at least 74.
0.3694
A certain medical test is known to detect 72% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?
1) binom.dist(x, n, p, 0). = .0374 2) 1 -binom.dist(7,10,0.72,1) = .4378 3) binom.dist (4,10,.72,1) = .0342
Points: 10 out of 10 The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: x 0 1 2 3 4 5 P(X = x) 0.20 0.30 0.20 0.15 0.10 0.05 On average, how many accidents are there in the intersection in a week?
1.8
Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds. What is the completion time for the 200-meter backstroke for a female with a z-score of −1.64? (Round answer to 1 decimal place.)
129.5
The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 14. According to the standard deviation rule, only % of people have an IQ over 114.
16
Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4. After she rolls it 33 times, Joan finds that she's rolled the number 4 a total of six times. What is the empirical probability that Joan rolls a 4?
18.18%
The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of: μ= 324 and a standard deviation of: σ= 38. According to the standard deviation rule, almost 2.5% of the students spent more than what amount of money on textbooks in a semester?
2.5%= more than= add 2 times whatever the sd is answer:400
In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of these show some signs of damage. Which of the following statements is correct?
40% is a statistic
Here are the number of hours that 9 students spend on the computer on a typical day: 4 5 5 5 8 8 10 12 13 What is the mode number of hours spent on the computer?
5
Based on the results of a nationwide study, the number of contacts programmed into cell phones are summarized on the following boxplot: Which interval contains the greatest amount of data?
50-100
In June 2015, Gallup conducted a poll of a random sample of 15759 adults to determine the well-being of people living in the United States. One question asked, "Did you exercise at least 30 minutes for 3 or more days in the past week?" In the survey, 55.3% of males and 44.7% of females responded yes to this question. Which of the following is true about this scenario?
55.3% and 44.7% are both statistics.
Based on the histograms, what is the most likely value of the population mean?
8
The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 13. According to the standard deviation rule, % of people have an IQ between 61 and 139.
99.7
A 2009 study analyzed data from the National Longitudinal Study of Adolescent Health. Participants were followed into adulthood. Each study participant was categorized as to whether they were obese (BMI >30) or not and whether they were dating, cohabiting, or married. The researchers were trying to determine the effect of relationship status on obesity. The table below summarizes the results. In this example, which of the following would it be appropriate to calculate?
Conditional column percentages
Suppose that P(A) = 0.96. Which of the following is the best interpretation of this statement?
Event A is extremely likely, but in a long sequence of trials, it occasionally will not occur.
Does secondhand smoke increase the risk of a low weight birth? A baby is "low birth weight" if it weighs less than 5.5 pounds at birth. According to the National Center of Health Statistics, about 7.8% of all babies born in the U.S. are categorized as low birth weight. Researchers randomly select 1200 babies whose mothers had extensive exposure to secondhand smoke during pregnancy. 10.4% of the sample are categorized as low birth weight. Which of the following are the appropriate null and alternative hypotheses for this research question.
H0: p = 0.078; Ha: p > 0.078
A politician claims that a larger proportion of members of the news media are Democrats when compared to the general public. Let p1 represent the proportion of the news media that is Democrat and p2 represent the proportion of the public that is Democrat. What are the appropriate null and alternative hypotheses that correspond to this claim?
H0: p1 - p2 = 0; Ha: p1 - p2 > 0
The outlier on the graph is likely due to an error in recording the data. Which of the following statements is true?
If the outlier were removed, the correlation coefficient (r) would increase
Let A and B be two independent events. If P(A) = 0.5, what can you say about P(A | B)?
It is equal to 0.5.
Which class has a greater percentage of estimates between 50 and 100 marshmallows?
Ms. Banana's class
In 2011, the Institute of Medicine (IOM), a non-profit group affiliated with the US National Academy of Sciences, reviewed a study measuring bone quality and levels of vitamin-D in a random sample from bodies of 675 people who died in good health. 8.5% of the 82 bodies with low vitamin-D levels (below 50 nmol/L) had weak bones. Comparatively, 1% of the 593 bodies with regular vitamin-D levels had weak bones. Is a normal model a good fit for the sampling distribution?
No, there are not at least 10 people with weak bones and 10 people with strong bones in each group.
According to the information that comes with a certain prescription drug, when taking this drug, there is a 18% chance of experiencing nausea (N) and a 48% chance of experiencing decreased sexual drive (D). The information also states that there is a 11% chance of experiencing both side effects. What is the probability of experiencing only nausea?
P(N)-P(both)= .18-.11= .07
Which of the following is the best description of the relationship between X and Y as it appears in the scatterplot?
Positive linear relationship with outlier(s)
Which of the following is an example of stratified sampling?
Proponents of a local ballot measure conduct a survey of the city by randomly selecting 100 potential voters from each of its 18 zip codes.
The makers of Mini-Oats cereal have an automated packaging machine that is set to fill boxes with 24.3 ounces of cereal (as labeled on the box). At various times in the packaging process, we select a random sample of 100 boxes to see if the machine is (on average) filling the boxes as labeled. On Tuesday morning, at 7:45 a.m., a random sample of 100 boxes produced an average amount of 23.7 ounces. Which of the following is an appropriate statement of the null hypothesis?
The machine fills the boxes with the proper amount of cereal. The average is 24.3 ounces (H0: μ = 24.3)
Suppose that the correlation r between two quantitative variables was found to be r=0. Which of the following is the best interpretation of this correlation value?
There is no linear relationship between the two variables.
When conducting a survey, which of the following is the most important reason to use a random sample?
To avoid bias and to get a representative sample
In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They surveyed a random sample of 1914 cell phone users. 75% of the sample use text messaging. The 95% confidence interval is (73.1%, 76.9%). Which of the following is an appropriate interpretation of the 95% confidence interval?
We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.
Determine if the following could be a probability distribution for a discrete random variable, X. If no, state why. X 3 6 9 12 15 P(X=x) 4/9 2/9 1/9 1/9 1/9
Yes, the probabilities associated with each X are all positive and they all add up to 1.
Find the p-value for the hypothesis test. A random sample of size 50 is taken. The sample has a mean of 420 and a standard deviation of 81.H0: µ = 400Ha: µ > 400 The p-value for the hypothesis test is
h0 = 400 hA = > 400 xbar = 420 n = 50s = 81 se = s/ sqrt(n) t=standardize(xbar, h0, se) p val = t.dist.rt(t , n-1) 0.0435
The difference between teenage female and male depression rates estimated from two samples is 0.06. The estimated standard error of the sampling distribution is 0.04. What is the 95% confidence interval? Use the critical value z = 1.96.
p1 - p2 = 0.06 SE = 0.04 z = 1.96 MOE = z * S lower = 0.06 - MOE upper = 0.06 + MOE = -0.02, 0.14
What type of variable is age?
quantitative
A researcher wants to determine if preschool attendance is associated with high school graduation for low-income students. She randomly assigns low-income children to two groups; one group will attend preschool program, the second group will not attend preschool. The researcher plans to follow the children in the study for 20 years and observe whether or not they graduate from high school. Which of the following is the response variable in this study?
whether or not a subject graduates highschool
In 2015 as part of the General Social Survey, 1263 randomly selected American adults responded to this question: "Some countries are doing more to protect the environment than other countries. In general, do you think that America is doing more than enough, about the right amount, or too little?" Of the respondents, 489 replied that America is doing about the right amount. What is the 95% confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment. (0.36, 0.414) (0.365, 0.41) (0.352, 0.422) (0.373, 0.401)
(0.36, 0.414)
The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and universities. Suppose we take a poll (random sample) of 3532 students classified as Juniors and find that 3117 of them believe that they will find a job immediately after graduation. What is the 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation. (0.874, 0.891) (0.872, 0.893) (0.869, 0.896) (0.877, 0.888)
(0.869, 0.896)
Let A and B be two disjoint events such that P(A) = 0.53 and P(B) = 0.29. What is P(A and B)?
0
The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might expect in a sample of 1000 students that the number of students with heights less than 163 cm is:
23
The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of 479 and a standard deviation of 21. According to the standard deviation rule, approximately 99.7% of the students spent between $ -----and $----- on textbooks in a semester.
99.7% = add/ subtract 3 times whatever the sd is lower: 416 upper: 542
A factory produces plate glass with a mean thickness of 4mm and a standard deviation of 1.1mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of the 100 sheets is to be computed. What is the probability that the average thickness of the 100 sheets is less than 3.74 mm?
= 1.1/ sqrt(100) = 0.11 = norm.dist(3.74, mean, 0.11, 1) = .00905
Suppose that 90% of all dialysis patients will survive for at least 5 years. In a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?
=sqrt (.90*(1-.90)/100) to find sd= .03 then 1-norm.dist (.80,.90,sd,1) =.99957
A recent survey asks 83 students, How many hours do you spend on the computer in a typical day? Of the 83 respondents, 3 said 1 hour, 4 said 2 hours, 10 said 3 hours, 21 said 4 hours, 19 said 5 hours, 16 said 6 hours, 6 said 7 hours, 3 said 8 hours, 1 said 9 hours. What is the average (mean) number of hours spent on the computer?
=sumproduct(x,y) answer divide by number of students so 83
The faculty senate at a large university wanted to know what proportion of the students thought foreign language classes should be required for everyone. The statistics department offered to cooperate in conducting a survey, and a simple random sample of 500 students was selected from all the students enrolled in statistics classes. A survey form was sent by email to these 500 students. In this case, which of the following is the population of interest?
All students at the university.
Which of the following scenarios are Binomial?
An engineer chooses a SRS of 10 switches from a shipment of 10,000 switches. Suppose 10% of the switches in the shipment are bad. The engineer counts the number X of bad switches in the sample. You observe the sex of the next 20 children born at a local hospital: X is the number of girls among them.
Students in a discussion of gun control in a sociology class at Foothill Community College argue that Republicans are more likely to oppose gun control than Independents. They use data from an article titled "Gun Control Splits America," published March 23, 2010 in pewresarch.org by the Pew Research Center for the People and the Press. In this study 62% of Republicans and 57% of Independents say that states should not be able to pass laws banning handguns. For a claim that a larger proportion of Republicans oppose state laws banning handguns when compared to Independents, the null and alternative hypotheses are The p-value is 0.06. If we conduct this test at a 5% level of significance, what would be an appropriate conclusion?
Fail to Reject H0 , do not support Ha .
An urn contains 16 red marbles, 35 blue marbles, and 40 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red or a blue marble?
For events A and B, P(A or B) = P(A) + P(B) - P(A and B). P(Red or Blue) = 16/91 + 35/91 - 0 P(Red or Blue) = 0.5604
In the article "Foods, Fortificants, and Supplements: Where Do Americans Get Their Nutrients?" researchers analyze the nutrient and vitamin intake from a random sample of 16,110 U.S. residents. Researchers compare the level of daily vitamin intake for vitamin A, vitamin B-6, vitamin B-12, vitamin C, vitamin D, vitamin E and calcium. Unless otherwise stated, all hypothesis tests in the study are conducted at the 5% significance level. Researchers conduct a hypothesis test to determine if the proportion of U.S. residents consuming recommended levels of calcium is different among women and men. The p-value is 0.035, and researchers conduct this test at a 5% level of significance. What does a p-value of 0.035 mean?
If calcium consumption is the same for women and men, there is a 3.5% chance that future studies will show differences in calcium consumption greater than observed in this study.
A researcher conducts an experiment on human memory and recruits 15 people to participate in her study. She performs the experiment and analyzes the results. She uses a t-test for a mean and obtains a p-value of 0.17. Which of the following is a reasonable interpretation of her results?
If there is a treatment effect, the sample size was too small to detect it.
Suppose that the handedness of the last fifteen U.S. presidents is as follows: 40% were left-handed (L) 47% were Democrats (D) If a president is left-handed, there is a 13% chance that the president is a Democrat. Based on this information on the last fifteen U.S. presidents, is "being left-handed" independent of "being a Democrat"?
No, since 0.47 is not equal to 0.13.
A study seeks to answer the question, "Does Vitamin C level in the breast milk of new mothers reduce the risk of allergies in their breastfed infants?" The study concluded that high levels of vitamin C (measured in mg) were associated with a 30 percent lower risk of allergies in the infants. In this scenario, "levels of vitamin C (measured in milligrams)" is what type of variable?
Quantitative
The histogram below displays the distribution of 50 ages at death due to trauma (accidents and homicides) that were observed in a certain hospital during a week. Which of the following best describes the shape of the histogram?
Right-skewed with a possible outlier
According to a 2014 research study of national student engagement in the U.S., the average college student spends 17 hours per week studying. A professor believes that students at her college study less than 17 hours per week. The professor distributes a survey to a random sample of 80 students enrolled at the college. From her survey data the professor calculates that the mean number of hours per week spent studying for her sample is: ¯x= 15.6 hours per week with a standard deviation of s = 4.5 hours per week. The professor chooses a 5% level of significance. What can she conclude from her data?
The data supports the professor's claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.
Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)? Check all that apply.
The distribution will be normal as long as the population distribution is normal. The distribution's mean is the same as the population mean 60.
Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. H0: The food is safe. Ha: The food is not safe Based on the hypotheses above, Is the following statement a Type I or Type II error? The sample suggests that the food is safe, but it actually is not safe.
Type II
Confidence interval precision: We know that narrower confidence intervals give us a more precise estimate of the true population proportion. Which of the following could we do to produce higher precision in our estimates of the population proportion?
We can select a lower confidence level and increase the sample size.
In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply.
We take repeated random samples of size 15 from a population that is normally distributed. We take repeated random samples of size 50 from a population of unknown shape.
According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing H0: p = 0.173 versus Ha: p < 0.173. The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth graders surveyed had used marijuana. Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?
Yes, because (80)(.173) and (80)(1 ‑ 0.173) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions.
The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule. (a) What proportion of the students scored at least 20 points on this test, rounded to five decimal places? (b) What is the 42 percentile of the distribution of test scores, rounded to three decimal places?
a). 1-Norm.Dist(x, mean, standard deviation, 1) =.84134 b). NORM.INV(0.42, mean, standard deviation). = 21.596
A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 0.75 days with an approximately normal distribution. (a) Find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places. (b) Find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.
a). Norm.Dist(6,mean, standard deviation, 1) - Norm.Dist(5,mean, standard deviation ,1) = .03309 b). 1 - norm.dist(x,mean, standard deviation ,1). =.96613
Cheating: For a statistics project a community college student at Diablo Valley College (DVC) decides to investigate cheating in two popular majors at DVC: business and nursing. She selects a random sample of nursing and business courses and convinces the professors to distribute a short anonymous survey in their classes. The question about cheating is one of many other questions about college life. When the student summarizes the data, she finds that 42 of the 50 business students and 38 of the 70 nursing students admitted to cheating in their courses. True or false? The counts suggest that the normal model is a good fit for the sampling distribution of sample differences.
false
The package of a particular brand of rubber band says that the bands can hold a weight of 7 lbs. Suppose that we suspect this might be an overstatement of the breaking weight. So we decide to take a random sample of 36 of these rubber bands and record the weight required to break each of them. The mean breaking weight of our sample of 36 rubber bands is 6.6 lbs. Assume that the standard deviation of the breaking weight for the entire population of these rubber bands is 2 lbs. True or false? Finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely.
false
A group of 74 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73.The group of 74 students in the study reported an average of 4.60 drinks per with a standard deviation of 3.81 drinks.Find the p-value for the hypothesis test
h0 = 4.73h A = not 4.73 xbar = 4.6 std = 3.81n = 74 SE = std / sqrt(n) t = standardize(xbar, h0, SE) p val = t.dist.2t(abs(t),n-1) = 0.7700
Commute times in the U.S. are heavily skewed to the right. We select a random sample of 500 people from the 2000 U.S. Census who reported a non-zero commute time.In this sample, the mean commute time is 28.4 minutes with a standard deviation of 18.9 minutes. Can we conclude from this data that the mean commute time in the U.S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance.What is the p-value for this hypothesis test?
h0= 30 hA = < 30 xbar= 28.4 n= 500 s=. 18.9 se=. s/ sqrt(n) t=standardize(xbar, h0, se) p val = t.dist(t, n-1, 1) *** use t.dist when its asking for LESS THAN = 0.0295
A florist determines the probabilities for the number of flower arrangements they deliver each day. x 19 20 21 22 23 P(x) 0.20 0.24 0.31 0.13 0.12 Find the mean, variance, and standard deviation of the distribution rounded to 4 decimal places.
mean: =sumproduct(x,Y) 20.73 Variance: =sumproduct(x^2,y)-mean^2 1.5771 SD: sqrt variance 1.2558 last part multiply 20.73 (mean) by 7 days
Which class has greater variability in students' estimate of the number of marshmallows?
ms apples class
According to a Pew Research Center study, in May 2011, 40% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 445 community college students at random and finds that 221 of them have a smart phone. Then in testing the hypotheses:H0: p = 0.4 versusHa: p > 0.4,what is the test statistic?
n = 445x = 221 phat = 221/445 p = 0.4 se = sqrt(p(1-p)/n) z= standardize(phat, p ,se) = 4.16
Let A and B be two disjoint events such that P(A) = 0.09 and P(B) = 0.54. What is P(A or B)?
p(A)+P(B)= .63
Let A and B be two independent events such that P(A) = 0.32 and P(B) = 0.58. What is P(A or B)?
p(A)+p(B)-p(A*B) =.7144
According to the information that comes with a certain prescription drug, when taking this drug, there is a 17% chance of experiencing nausea (N) and a 43% chance of experiencing decreased sexual drive (D). The information also states that there is a 10% chance of experiencing both side effects. What is the probability of experiencing neither of the side effects?
p(N)+P(D)-p(NnD)= .17+.43-.10= .50
Previous studies suggest that use of nicotine-replacement therapies and antidepressants can help people stop smoking. The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment.In this experiment researchers randomly assigned smokers to treatments. Of the 178 smokers taking a placebo, 31 stopped smoking by the 8th day. Of the 267 smokers taking only the antidepressant buproprion, 88 stopped smoking by the 8th day. Calculate the estimated standard error for the sampling distribution of differences in sample proportions.The estimated standard error =
p1= 31/178 n1=178 p2=88/267 n2=267 se = sqrt(p1(1-p1)/n + p2(1-p2)/n) = 0.040
In a study at West Virginia University Hospital, researchers investigated smoking behavior of cancer patients to create a program to help patients stop smoking. They published the results in Smoking Behaviors Among Cancer Survivors (January 2018, Journal of Oncology Practice). In this study, the researchers sent a 22-item survey to 1499 cancer patients. They collected demographic information (age, sex, ethnicity, zip code, level of education), clinical and smoking history, and information about quitting smoking.Of the 1499 patients who were mailed surveys, 300 patients responded. For various reasons, researchers used only 270 of the completed surveys. 44 out of 147 female cancer patients reported being past smokers, and 80 out of 123 male cancer patients reported being past smokers. Calculate the difference between the corresponding sample proportions ^p1−^p2 (female minus male). Round the answer to 4 decimal places.
p1= 44/147p2 = 80/123 then do p1-p2 = -0.3511
Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a simple random sample (SRS) of 35 students from this distribution. What is the probability that a SRS of 35 students will spend an average of between 600 and 700dollars? Round to five decimal places.
sd = 120 / sqrt(30) = norm.dist(700, mean, sd, 1) - norm.dist(600, mean, sd, 1) =.98630
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let ^p denote the proportion in the sample who say they support the increase. Suppose that 29% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is
sd = sqrt(0.29 *(1-0.29)/ 1500) 0.0117
In 2014, students in an advanced Statistics course at UC Berkeley conducted an anonymous survey about use of cognition-enhancing drugs among college males. One survey group of males included members from a fraternity, and the other survey group of males included no fraternity members. The standard error formula for the difference between sample proportions is Calculate the standard error for a survey comparing proportions of cognition-enhancing drug use of fraternity members to non-fraternity members, where p1 = 0.32, n1 = 107, p2 = 0.26, n2 = 92. Round all calculations to the thousandth decimal place.
se = sqrt(p1(1-p)/n1 + p2(1-p2)/n2) =.064
Which of the following variables is discrete? Check all that apply.
shoe size dress size
A researcher took a random sample of 100 students from a large university. She computed a 95% confidence interval to estimate the average weight of the students at this university. The confidence interval was too wide to provide a precise estimate. True or false? The researcher could produce a narrower confidence interval by increasing the sample size to 150.
true
In the population, 8% of males have had a kidney stone. Suppose a medical researcher randomly selects two males from a large population. Let A represent the event "the first male has had a kidney stone." Let B represent the event "the second male has had a kidney stone." True or false? A and B are independent events.
true
The city council hired three college interns to measure public support for a large parks and recreation initiative in their city. The interns mailed surveys to 500 randomly selected participants in the current public recreation program. They received 150 responses. True or false? Even though the sample is random, it is not representative of the population of interest.
true
Which one of the three random variables has the largest standard deviation?
v
A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 47 cables and apply weights to each of them until they break. The 47 cables have a mean breaking weight of 777.4 lb. The standard deviation of the breaking weight for the sample is 15.5 lb. Find the 90% confidence interval to estimate the mean breaking weight for this type cable.
x bar = 777.4 n = 47 s = 15.5 st error = 15.5 / sqrt(47)t = t.inv.2t(0.10,46) MOE = T * SE lower = MOE - XBAR upper = MOE + XBAR (773.60 , 781.20)
The SAT is the most widely used college admission exam. (Most community colleges do not require students to take this exam.) The mean SAT math score varies by state and by year, so the value of µ depends on the state and the year. But let's assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year. More specifically, assume that individual SAT math scores consistently have a normal distribution with a standard deviation of 100. An educational researcher wants to estimate the mean SAT math score (μ) for his state this year. The researcher chooses a random sample of 698 exams in his state. The sample mean for the test is 490.Find the 90% confidence interval to estimate the mean SAT math score in this state for this year.(Note: The critical z-value to use, zc, is: 1.645.)
xbar. - 490 n. - 698 sigma - 100 st error - = 100/ sqrt(698) z - 1.645 moe - 1.645 * St error lower = xbar - MOE upper = xbar + MOE (483.774, 496.226)
In the article "Attitudes About Marijuana and Political Views" (Psychological Reports, 1973), researchers reported on the use of cannabis by liberals and conservatives during the 1970s. To test the claim (at 1% significance) that the proportion of voters who smoked cannabis frequently was lower among conservatives, the hypotheses were Suppose that we conduct a hypothesis test in which a Type II error is very serious. But the Type I error is not very serious. Which level of significance is the best choice?
α = 0.05