Statistics Questions and Answers

A newsgroup is interested in constructing a 99% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 518 randomly selected Americans surveyed, 397 were in favor of the initiative. a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between ... and .... Round to 3 decimal places. b. If many groups of 518 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About ... percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about ... percent will not contain the true population proportion.

Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 1033 parents of children ages 8-14, 73% say they are willing to get a second or part time job to pay for their children's college education and 45% say they lose sleep worrying about college costs. The survey's margin of error is ±2%. Use the results from the survey about getting a second or part-time job.

A researcher wishes to estimate, with 95% confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within 3% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 22% of the respondents said they eat fast food four to six times per week. (c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? n= (Round up to the nearest whole number as needed.)

[8 points] The Pew Research Center estimates that as of January 2014, 89% of 18-29 year olds in the United States use social networking sites. Calculate the probability that at least 91% of 500 randomly sampled 18-29 year olds use social networking sites.

[6 pts] ACT, Inc. reported that 74% of 1644 randomly selected college freshmen returned to college the next year. a. Construct and interpret a 90% confidence interval to estimate the retention rate for college freshmen. b. They want a margin of error of 1%. How many college freshmen must be surveyed?

A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.12 lb, the mean of all of the weights is x=2.172 lb, and the standard deviation of the weights is s= 1.931 lb. a. What is the difference between the weight of 5.12 lb and the mean of the weights? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the weight of 5.12 lb to a z score. d. If we consider weights that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, is the weight of 5.12 lb significant? a. The difference is lb. (Type an integer or a decimal. Do not round.)

In a survey of 1033 parents of children ages 8-14, 73% say they are willing to get a second or part-time job to pay for their children's college education and 45% say they lose sleep worrying about college costs. The survey's margin of error is ±2% Use the results from the survey about getting a second or part-time job. The confidence interval for the proportion is (). (Round to three decimal places as needed.) Use the results from the survey about getting a second or part-time job. The interval is a % confidence interval. (Round to one decimal place as needed.) Use the results from the survey about losing sleep. The confidence interval for the proportion is (Round to three decimal places as needed.)

Luke took a survey of the age of six students in his college class. Their ages were 21, 22, 21, 24, 21, and 23. Luke found the mean, median, mode, and range. Which of these four measures has the highest value? mean median mode range

In a random sample of 25 people, the mean commute time to work was 32.6 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a t-distribution to construct a 80% confidence interval for the population mean µ. What is the margin of error of µ? Interpret the results.

A hotdog vendor must pay a monthly fee to operate a food cart in the city park. The cost in dollars of selling x hundred hotdogs in a month can be approximated by C(x)=170+85x. Complete parts (a) through (d) below. (a) Find the average-cost function

Find the following probability using the standard normal distribution. P(z < 1.7) Select the correct answer below: 0.5431 0.8659 0.9554 0.7659

The life of a Radio Shack record player is normally distributed with a mean of 3.3 years and a standard deviation of 0.8 years. Radio Shack guarantees its record players for 2 years. Find the probability that a record player will break down during the guarantee period. 0.04218 0.03417 0.05208 0.03796 0.06302 0.05729 0.04687

Which of the following is not a discrete random variable? Multiple Choice the number of times a light changes red in a 10-minute cycle the number of minutes required to run 1 mile the number of defects in a sample selected from a population of 100 products the number of criminals found in a five-mile radius of a neighborhood

Listed below in order are prices in dollars for a Big Mac hamburger in the United States, Canada, Mexico, China, Japan, Russia, Switzerland, Italy, Spain, Britain, India, and Egypt. Such data are used to compare currency exchange rates and the costs of goods in different countries. Find the range, variance, and standard deviation for the given sample data. What do the measures of variation tell us about the prices of a Big Mac in different countries? 5.28 5.31 2.60 3.19 3.42 2.30 6.79 5.12 4.81 4.42 2.76 1.86 The range is (Type an integer or decimal rounded to two decimal places as needed.) The variance is (Type an integer or decimal rounded to two decimal places as needed.)

The amount of time to complete a physical activity in a PE class is approximately normally distributed with a mean of 34.7 seconds and a standard deviation of 6.9 seconds. a) What is the probability that a randomly chosen student completes the activity in less than 29.7 seconds? b) What is the probability that a randomly chosen student completes the activity in more than 40.7 seconds? c) What proportion of students take between 31 and 40.4 seconds to complete the activity? d) 75% of all students finish the activity in less than 44.71 seconds.

The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. Find the mean, median, mode, and standard deviation. Round to one decimal place as needed. 20, 22, 25, 28, 29, 32, 33, 33 Mean Median Mode Standard Deviation

You are 18 years old, opening your first savings account, and are considering three options: BANK A is not FDIC insured, has an interest rate of 5%, and a minimum deposit of $25. BANK B is FDIC insured, has an interest rate of 0.01%, and a minimum deposit of $50. BANK C is FDIC insured, has an interest rate of 0.02%, and a minimum deposit of $10,000. All three have fees competitive with other banks. Which bank is the best option? Bank A Bank B Bank C All 3 banks are equally good options

Which statistic (mean, median, or mode) is most appropriate in each of the following situation? Tables in the dining hall are numbered 1-12 for students who eat there. The principal calls out a number for the table that will go through the buffet line first. The other tables follow in order of the table numbers. One student is sure the principal calls certain tables more often. She keeps track of which numbers are called over a 21-day period. Mean Median Mode

The first advertisement discussed in class states that the salespeople make an average of $1,000 per week. Suppose there are nine salespeople. What would the ninth person need to earn for the mean to be $1,000 if the other eight salespeople earned $550, $600, $600, $800, $950, $950, $1,000, and $1,100?

The 8 students in Mrs. Barnes' class were asked how many minutes it takes them to get to school in the morning. Here is what they answered: 6, 11, 10, 14, 15, 4, 13, 4 Find the mean and median travel times for these students. If necessary, round your answers to the nearest tenth. Mean: minutes Median: minutes

One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman who has $138,400 to invest would like to have an income of $18,720 per year from her investments. How much should she invest at each rate?

54. At the school carnival, Ann is playing a game involving a stack of 10 index cards. Each card has a single number written on it: 1 card has a 1, 2 cards have a 2, 3 cards have a 3, and 4 cards have a 4. Ann will choose 1 card at random, and she will be awarded the number of points equal to the number written on the card. Let the random variable X represent the number of points Ann receives on any 1 draw. What is the expected value of X ? E. 0.4 G. 1 H. 2.5 J. 3 K. 4

A bank randomly selected 248 checking account customers and found that 111 of them also had savings accounts at this same bank. Construct a 95% confidence interval for the true proportion of checking account customers who also have savings accounts. (Round your answers to three decimal places.) lower limit upper limit

The Thundering Herd, an amusement park ride, is not open to patrons less than 54" tall. If the mean height of park patrons is 68" with a standard deviation of 12 inches, what percent of the patrons will not be able to use this ride? The z for 54" = - The percentage for the above z is This is the percentage of patrons between 54" and 68". The percentage for ALL patrons above 68" is %So the percentage of patrons above 54" is %.Therefore, adding the two together, the percentage of patrons below 54" and who maynot use this ride is %.

Salma wants to find the average height of students in the 12th grade at West High School. So she will use the heights of 44 students in the 12th grade to find the average height. Answer the questions below. (a) Which unit(s) could be used for the unit of measurement? Check all that apply. pounds ounces centimeters grams inches (b) Which of the procedures below would be the best way to find the average height? Measure the heights of 44 volunteers from the 12th grade. Ask for 44 volunteers from the 12th grade to state their own heights. Randomly pick 44 students from the 12th grade and have them state their own heights. Randomly pick 44 students from the 12th grade and measure their heights.

(a) A botanist at a nursery wants to inspect the health of the plants at the nursery. Which of the following best describes a systematic sample of plants? The botanist forms 6 groups of plants based on the ages of the plants (in months). Then, he selects 12 plants at random from each group. The botanist assigns each plant a different number. Using a random number table, he draws 72 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 72 plants is equally likely to be drawn using the random number table. The botanist takes a list of the plants and selects every 3rd plant until 72 plants are selected. (b) A chemist at a pharmaceutical company wants to test the quality of a new batch of microscopes. Which of the following best describes a convenience sample of microscopes? The chemist assigns each microscope a different number. Using a random number table, he draws 64 of those numbers at random. Then, he selects the microscopes assigned to the drawn numbers. Every set of 64 microscopes is equally likely to be drawn using the random number table. The microscopes in the first shipment that was received are easily accessible. So, he selects all 64 the microscopes in this shipment. The chemist takes a list of the microscopes and selects every 4th microscope until 64 microscopes are selected. (c) A facilities supervisor at a sports stadium wants to rate the condition of the seats at the stadium. Which of the following best describes a stratified sample of seats? The supervisor forms 6 groups of seats based on the dates the seats were last replaced. Then, she selects 9 seats at random from each group. The supervisor forms groups of 9 seats based on the sections the seats are in. Then, she selects all of the seats in 6 randomly chosen groups. All of the seats in the VIP section are easily accessible. So, the supervisor selects the 54 seats in this section. O O X

c) A facilities supervisor at a sports stadium wants to rate the condition of the seats at the stadium. Which of the following best describes a stratified sample of seats? The supervisor forms 6 groups of seats based on the dates the seats were last replaced. Then, she selects 9 seats at random from each group. The supervisor forms groups of 9 seats based on the sections the seats are in. Then, she selects all of the seats in 6 randomly chosen groups. All of the seats in the VIP section are easily accessible. So, the supervisor selects the 54 seats in this section.

The lifetime of a certain brand of battery is known to have a standard deviation of 11.5 hours. Suppose that a random sample of 90 such batteries has a mean lifetime of 34.3 hours. Based on this sample, find a 95% confidence interval for the true mean lifetime of all batteries of this brand. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

Here are the shopping times (in minutes) for a sample of 5 shoppers at a particular grocery store. 26, 31, 35, 23, 20 Send data to calculator Find the standard deviation of this sample of shopping times. Round your answer to two decimal places. (If necessary, consult a list of formulas.)

A tour company in a major city has a daily sightseeing trip. Each day, tour officials record the number of people making the trip. The data for a selection of summer days are as follows. 43, 44, 33, 42, 31, 40, 47, 36, 30 (a) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. (b) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place. (c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the model(s), if applicable.

An investment company advertised that last year its clients, on average, made a profit of 9%. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements is true, mark the appropriate box. Last year at least one of their clients made a profit of exactly 9%. Two years ago some of their clients made a profit of at least 9%. Last year, the number of their clients who made a profit of 9% or more was equal to the number of their clients who made a profit of 9% or less. Last year all of their clients made a profit of at least 9%. Last year at least one of their clients made a profit of less than 15%. None of the above statements are true. X Ś ?

In which of the following circumstances would a post-hoc test (e.g., Tukey's HSD) be used? when the F-ratio is not significant when Ho is rejected and there are more than two treatments when there are two treatments post hoc tests should always be conducted after an ANOVA

A researcher predicts that dog owners living in the rural area spend different amount of time walking their dogs as compared to dog owners living in the city. The researcher gets a sample of 20 dog owners in the rural area and 22 dog owners in the city. The mumber of hours per week that an owner spends walking his or her dog is recorded. The data are as follows: Dog Owners in the rural area M = 15 SS=320 n=20 Dog owners in the city M = 10 SS=205 n=22 a.State the null hypothesis and the alternative hypothesis in symbol b. Test the hypothesis using a = .05

In a certain city of several million people, 5.7% of the adults are unemployed. If a random sample of 280 adults in this city is selected, approximate the probability that at least 12 in the sample are unemployed. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.)

A study measured the average rainfall in 130 months in the state of Hawaii. The average monthly rainfall was 3.7 inches with a standard deviation of 0.3 inches. Assume the data is normally distributed. How many months of rainfall had more than 4 inches of rainfall? 68 months 14 months 21 months 112 months 34 months

Find the sample group of the following example: Darwin asks every person at the city's baseball game what their favorite sport is to find out the most popular sport in the city. Every person at the baseball game All sports Every person in the city Darwin asking people questions

A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 52.5% of them have an IQ score over 100. It is known that 50% of the general population has an IQ score exceeding 100. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where is the proportion of people with IQ scores over 100 in a random sample of 400 people. (b) Find the standard deviation of p. (c) Compute an approximation for P(≥0.525), which is the probability that there will be 52.5% or more individuals with IQ scores over 100 in a random sample of 400. Round your answer to four decimal places.

A brokerage survey reports that 36% of all individual investors have used a discount broker (one that does not charge the full commission). If a random sample of 150 individual investors is taken, approximate the probability that at least 56 have used a discount broker. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.) 0.688 ?

In a grade 5 classroom the numbers 1 to 100 are written on the chalkboard. The teacher circles 10 numbers at random. What is the expected number of prime numbers that will be circled by the teacher? 5 prime numbers 7.5 prime numbers 10 prime numbers 2.5 prime numbers

The manager of the local coffee shop is surveying her customers to determine if they prefer room for cream or no room for cream in their coffee cup. The results showed that 40% would like room for cream in their coffee cup with a 10% margin of error. How many customers did the manager survey? 82 10 48 50 96

Suppose that the lifetimes of TV tubes are normally distributed with a standard deviation of 1.2 years. Suppose also that exactly 35% of the tubes die before 4.5 years. Find the mean lifetime of TV tubes. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

Shandra bought some belts online for $67. She used a coupon code to get a 20% discount. The website also applied a 5% processing fee to the price after the discount. How much was the discount, in dollars and cents?

A Pew Research report indicated that 73%, of teenagers aged 13-17 own smartphones. A random sample of 150 teenagers is drawn. Find the probability that more than 70% of the sampled teenagers own a smartphone.

Which of the following would result in a confidence interval with a larger width? using a smaller sample obtaining a sample with lower variability selecting a smaller % confidence none of the above

An educator claims that the average salary of substitute teachers in New York is at most $100 per day. A random sample of ten school districts is selected, and the daily salaries are shown. Is there evidence to support the claim at a = .1? 85 70 110 95 90 102 87 78 69 100

The spinner on a wheel of fortune can land with an equal chance on any one of ten regions. Three regions are red, four are blue, two are yellow, and one is green. A player wins $5 if the spinner stops on red and $3 if it stops on green. The player loses $2 if it stops on blue and $5 if it stops on yellow. a. What is the expected value?

In a distribution where the mean is 80 and the standard deviation is 3, find the largest fraction of the numbers that could meet the following requirements. less than 74 or more than 86 Of the numbers in the distribution, the fraction that is less than 74 or more than 86 is at most

A newspaper article states with 95% confidence that 55% to 65% of all high school students in the United States claim that they could get a hand gun if they wanted one. This confidence interval is based on a poll of 2000 high school students in Detroit. How would you interpret the confidence interval from this newspaper article? A. 95% of large urban cities in the United States have 55% to 65% high school students who could get a hand gun. B. If we took many samples of high school students from different urban cities, 95% of the samples would have between 55% and 65% high school students who could get hand guns. C. The newspaper incorrectly used this confidence interval to generalize to all teenagers in the United States since the sample was taken from the population of high school students in Detroit. D. We can be 95% confident that between 55% and 65% of all United States high school students could get a hand gun.

A 95% confidence interval is computed to estimate the mean household income for a city. Which of the following values will definitely be within the limits of this confidence interval? A. The population mean B. The sample mean C. The standard deviation of the sample mean D. None of the above

Justin is interested in buying a digital phone. He visited 10 stores at random and recorded the price of the particular phone he wants. The sample of prices had a mean of 332.88 and a standard deviation of 10.23. (a) What t-score should be used for a 95% confidence interval for the mean, μ, of the distribution? t* = (b) Calculate a 95% confidence interval for the mean price of this model of digital phone: (Enter the smaller value in the left answer box.) to