Stat Final Review
According to a Pew Research Center study, in May 2011, 33% 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 390 community college students at random and finds that 162 of them have a smart phone. Then in testing the hypotheses: H0: p = 0.33 versus Ha: p > 0.33, what is the test statistic?
#24 in notes
A florist determines the probabilities for the number of flower arrangements they deliver each day. P(x) and X 0.22 (19) 0.21 (20) 0.33 (21) 0.14 (22) 0.10 (23) Find the mean, variance, and standard deviation of the distribution rounded to 4 decimal places. Approximately how many arrangements should the florist expect to deliver each week, rounded to the nearest whole number?
Mean = SUMPRODUCT (X, P(x) ) Variance = SUMPRODUCT (X^2, P(x) ) - Mean^2 St. Dev. = sqrt (variance) Last part = Mean*7
The boxplots below show the number of marshmallows in a bag, as estimated by students in two elementary school classes. Which class has greater variability in students' estimate of the number of marshmallows?
Ms Apple's Class (blue area is longer)
The boxplots below show the number of marshmallows in a bag, as estimated by students in two elementary school classes. Which class has a greater percentage of estimates between 50 and 100 marshmallows?
Ms Banana's Class (shorter blue area)
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
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.
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
Three random variables, U, V, W have distributions as shown in the graphs below. Which one of the three random variables has the largest standard deviation?
V bc the rectangles at the end are farthest away
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.
Which of the following variables is discrete? Check all that apply.
- Shoe size - Dress size
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. Maybe more?
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 127 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. - The actual count of those who do not drive to campus is too small. - n(1−^p) is not greater than 10.
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 sample needs to be random, but we don't know if it is. - The actual count of community residents who received the concert brochure by mail is too small. - n^p is not greater than 10.
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.
Let A and B be two DISJOINT events such that P(A) = 0.01 and P(B) = 0.27. What is P(A and B)?
0 - A and B for disjoint is always 0
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 142.
0.15% (in notes)
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= 303 and a standard deviation of: σ= 26. According to the standard deviation rule, almost 0.15% of the students spent more than what amount of money on textbooks in a semester?
0.15% would make it three standard deviations away. So it would be 303+26+26+26 = 381
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
Here are the number of hours that 9 students spend on the computer on a typical day: 1 2 2 3 6 7 11 12 14 What is the mode number of hours spent on the computer?
2
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
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 bc the mean is between them
In June 2015, Gallup conducted a poll of a random sample of 15486 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, 59.3% of males and 40.7% of females responded yes to this question. Which of the following is true about this scenario?
59.3% and 40.7% are both statistics.
Pictured below (in scrambled order) are three histograms. One of them represents a population distribution. The other two are sampling distributions of x-bar: one for sample size n = 5 and one for sample size n = 40. Based on the histograms, what is the most likely value of the population mean?
8
The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with a mean of 481 and a standard deviation of 37. According to the standard deviation rule, approximately 95% of the students spent between $ _____ and $ _____on textbooks in a semester.
95% is two standard deviations so lower would be =481-2*37 and upper would be 481+2*37
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, ____ % of people have an IQ between 58 and 142. Do not round.
99.7% bc it is three standard deviations away - 95% would be two - 68% would be one
Look at the table below Score Count 2 [40-50) 2 [50-60) 5 [60-70) 5 [70-80) 3 [80-90) 1 [90-100) What percentage of students earned a grade of less than 60?
= (# less than 60)/(total)*100
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 2 a total of five times. What is the empirical probability that Joan rolls a 2?
= (5/33)*100 = 15.15%
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 away games). - 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
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 = 64 inches and the standard deviation is σ = 3.3 inches. Suppose we randomly sample 95 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?
= 3.3/sqrt(95) = 0.34
The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution: P(X = x) and x 0.20 (0) 0.30 (1) 0.20 (2) 0.15 (3) 0.10 (4) 0.05 (5) On average, how many accidents are there in the intersection in a week?
= SUMPRODUCT (X, P(X=x) )
An urn contains 15 red marbles, 34 blue marbles, and 43 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?
=(15+34)/(total marbles) = 0.5326
A recent survey asks 93 students, How many hours do you spend on the computer in a typical day? Of the 93 respondents, 2 said 1 hour, 7 said 2 hours, 12 said 3 hours, 21 said 4 hours, 22 said 5 hours, 15 said 6 hours, 7 said 7 hours, 5 said 8 hours, 2 said 9 hours. What is the average (mean) number of hours spent on the computer?
=SUMPRODUCT(#hours, #students)/93
What type of variable is color?
Categorial
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
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
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
A 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 obesity on relationship status. The table below summarizes the results: Calculate the row percentages for participants who were Not Obese .
Married: 425 Married and Not Obese: 278 To find the percentage you take (278/425)*100= 65.4%
Suppose that P(A) = 0.97. 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.\
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
Below is a probability distribution for the number of failures in an elementary statistics course. P(X=x) and X 0.42 (0) 0.16 (1) ? (2) 0.06 (3) 0.16 (4)
Find probability of 2 and go from there - Add the values together
Suppose that 70% 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?
Find st. dev first = sqrt(.70*(1-.70)/100) Then = 1-NORM.DIST (.80, .70, st.dev, 1)
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 4.03 mm?
First = 1.1/sqrt(100) Then = NORM.DIST (4.03, 4, first part, 1)
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 30 students from this distribution. What is the probability that a SRS of 30 students will spend an average of between 600 and 700 dollars? Round to five decimal places.
First = 120/sqrt(30) Then = NORM.DIST (700, 650, first part, 1) - NORM.DIST(600, 650, first part, 1) -
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
The weights (in pounds) and cholesterol levels (in mg/dL) of several individuals was observed. The data are shown in the scatterplot below: 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
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 3572 students classified as Juniors and find that 2905 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.
Like #66 except z will be 2.576
According to the information that comes with a certain prescription drug, when taking this drug, there is a 15% chance of experiencing nausea (N) and a 46% 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 only nausea?
Make a chart and fill it in
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 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?
Make a chart and fill it in
Let A and B be two INDEPENDENT events such that P(A) = 0.4 and P(B) = 0.4. What is P(A and B)?
P(A)*P(B) = 0.4 x 0.4 = 0.16
Let A and B be two INDEPENDENT events such that P(A) = 0.13 and P(B) = 0.77. What is P(A or B)?
P(A)+P(B) - P(A and B) = 0.13+0.77 - (0.13 x 0.77) = 0.7999
Let A and B be two DISJOINT events such that P(A) = 0.23 and P(B) = 0.46. What is P(A or B)?
P(A)+P(B)-P(A and B) =0.23+0.46 - 0 =
A certain medical test is known to detect 50% 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?
P(x=10) = BINOM.DIST (10,10, .50, 0) At least 8 = 1-BINOM.DIST(7, 10, .50, 1) At most 4 = BINOM.DIST (4, 10, .50, 1)
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 local ice cream shop kept track of the number of cans of cold soda it sold each day, and the temperature that day, for 2 months during the summer. The data are displayed in the scatterplot below: 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) - Straight positive line with one outlier
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.
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
Based on the results of a nationwide study, the number of contacts programmed into cell phones are summarized on the following boxplot: Choose the correct label for the point on the boxplot represented by the question mark:
Q3 the last line in the box
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 bc it's measured in milligrams
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.
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
A 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: Based on the table above, the percentage of Married participants, who were Not obese is: ____ %
Same as #18 - Total percentage is 100%
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
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.
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 23.9 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)
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.
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.
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?
This suggests that her experimental treatment has no effect on memory.
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
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 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%.
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.
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 high school
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.
Determine if the following could be a probability distribution for a discrete random variable, X. If no, state why. P(X=x) and X 4/9 (3) 2/9 (6) 1/9 (9) 1/9 (12) 1/9 (15)
Yes, the probabilities associated with each X are all positive and they all add up to 1.
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 19 points on this test, rounded to five decimal places? (b) What is the 29 percentile of the distribution of test scores, rounded to three decimal places?
a = 1-NORM.DIST (19, 22, 2, 1) b = NORM.INV ( .29, 22, 2)
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 1.50 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, 7.37, 1.50, 1) - (5, 7.37, 1.50, 1) b = 1-NORM.DIST(6, 7.37, 1.50, 1)
In 2015 as part of the General Social Survey, 1285 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, 459 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
phat = 459/1285 st. error = sqrt(phat*(1-phat)/1285) MOE = 1.96(z)*st.error lower =phat-MOE upper =phat+MOE
Estimating Mean SAT Math Score 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 658 exams in his state. The sample mean for the test is 495. Find the 95% confidence interval to estimate the mean SAT math score in this state for this year. (Note: The critical z-value to use, zc, is: 1.960.)
st error = 100/sqrt(658) MOE = z* st. error lower = 495- MOE upper = 495+MOE
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.
st error = 15.5 / sqrt(47) t= T.INV.2T(1- .90, 47-1) MOE = t*st. error lower = 777.4 - MOE upper = 777.4+ MOE