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STA2023 Study Union Final Exam ReviewMatch the definitions below with the following terms: variable, population, sample, inference.An estimate, prediction, or some other generalization about a population based on information contained in a sampleA set of all units that we are interested in studying (people, objects, etc.)A characteristic or property of an individual experimental (or observational) unit in the populationA subset of the populationDetermine which of the following describes a statistic or a parameter.Numerical summary of the populationNumerical summary of the sample dataUsually unknownFound from the sampleClassify each of the following data types required on a college application as either quantitative or qualitative.High school GPAHigh school class rankSAT or ACT scoreGenderParent’s incomeAgeBelow is a list of letter grades in a statistics class. Find the frequency and relative frequency of each class of data.AACBDBACFCDABBFABCCDFCFBGradesFrequencyRelative Frequency n = Calculate the mean, median, mode, variance, standard deviation, and range for the following sample data set:1216224112515Describe how the mean compares (=, >, <) with the median for a distribution as follows:Skewed to the leftSkewed to the rightSymmetric An industrial psychologist gave a subject two different tests designed to measure employee satisfaction (higher scores = higher satisfaction). Which score is better: a score of 57 on the first test, which has a mean of 72 and a standard deviation of 20, or a score of 450 on the second test, which has a mean of 500 and a standard deviation of 80? Explain.If my SAT score was in the 84th percentile, what percentage of people scored higher than me and what percentage scored lower than me?The following data is the number of hours 9 students spent studying for a test and their scores on that test. Hours Studying024555678Test Score405164697375939095Do you think a relationship would exist between the variables? Why or why not?Here is the scatter plot. What does it appear the relationship is between the variables?The correlation coefficient is r = 0.9685. Interpret the correlation.Using = .01, is there evidence the correlation is significant?If appropriate, find the equation of the regression line. ?CoefficientsIntercept37.44907hours7.451389If appropriate, use the regression equation to predict the test score for someone who studied 3 hours. If not appropriate, explain why not.If appropriate, use the regression equation to predict the test score for someone who studied 6.5 hours. If not appropriate, explain why not.If appropriate, use the regression equation to predict the test score for someone who studied 13 hours. If not appropriate, explain why not. Give the multiplicative rule of probability for:Two independent eventsAny two eventsThe following table describes the students at a large university. The students were classified according to their age and their college division. College DivisionLowerUpperTotalUnder 2014,4009,60024,000Age 20 – 25 12,00012,00024,000Over 25 4,800 7,20012,000Total31,20028,80060,000What is the probability of selecting a student under 20 years of age?What is the probability of selecting a student in the upper division?What is the probability of selecting a student over 25 years of age or a student in the upper division?What is the probability of selecting a student in the upper division, given the student is under 20 years of age?Are Upper and Over 25 mutually exclusive? Why? Show how you arrived at this conclusion. Determine which counting rule to use given the following conditions:Order mattersOrder does not matterNot everything is distinct A random sample of five students is to be selected from 50 sociology majors for participation in a special program. In how many different ways can the sample be taken? (pg. 176 #164) I have a group of 12 UCF students. In how many ways can I choose 6 of the students to participate in a special project if the first person picked is the president, the second VP, third treasurer, fourth historian, fifth secretary, sixth researcher?In how many ways can we rearrange the letters in the word STATISTICS? A poll of 15 voters is taken in a large city. The purpose is to determine x, the number in favor of a certain candidate for mayor. Suppose that 60% of all the city’s voters favor this candidate.Find the mean and standard deviation of x.Find the probability of at most 7 favoring.Find the probability of more than 10 favoring.The number of births per day at Arnold Palmer Hospital for Women and Children has a Poisson Distribution with mean 9. What is the probability that exactly 6 births would occur today?What is the probability that more than 7 births would occur today? If a measurement from a normal population possesses a negative z score, this implies that the measurement is __________ its mean. What does this notation denote: (0,1)?A machine pumps cleanser into a process at a rate of 7 gallons per minute. Upon inspection, it is learned that the machine pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 7.5 gallons per minute. What is the mean of this distribution? The standard deviation?Find the probability that the machine pumps less than 7 gallons during a randomly selected minute. A cigarette manufacturer claims that their latest low tar cigarette has a mean of 4.5 mg of tar per cigarette with a standard deviation of 1.2 mg. To check this claim, a consumer group will randomly select 300 cigarettes of this brand and measure the tar content in each. The mean of the sample of 300 tar measurements will be calculated.Assuming the manufactures claim is true, describe the sampling distribution of the sample mean. You should have 3 parts to your statement.Assuming tar content is normally distributed, what is the probability that a single cigarette will have a tar content greater than 4.7 mg?What is the probability that the sample mean will exceed 4.7 mg?The time between emergency room arrivals at a local hospital follow an exponential distribution with mean 5 minutes.Find the probability that the time between arrivals would be more than 8 minutes.Find the probability that the time between arrivals would be less than 2 minutes.The Goodyear Tire Company manufactures car tires that last distances that are normally distributed with a mean of 38,000 miles and a standard deviation of 4500 miles. If a tire is randomly selected, what is the probability it lasts more than 35000 miles?If 60 tires are randomly selected, what is sampling distribution of the sample mean?If 60 tires are randomly selected, what is the probability they last distances that have a mean greater than 37,500 miles?If the manufacturer wants to guarantee the tires so that only 4% will be replaced because of failure before the guaranteed number of miles, for how many miles should the tires be guaranteed?Sixteen loan applications in a bank were randomly selected and the dollar amount requested had a mean of $195,000 and a standard deviation of $45,000. Be sure to list any assumptions you make when constructing the intervalConstruct and interpret a 95% confidence interval for the mean dollar amount of all loans at the bank.Now, construct and interpret a 99% confidence interval for the mean dollar amount of all loans at the bank.In the 1991 General Social Survey, respondents were asked whether people convicted of murder should receive the death penalty. 1078 responded yes and 336 responded no. Construct a 99% confidence interval for the proportion of American adults who would answer yes. Interpret. Can you conclude that more than half of all American adults would answer yes? Why?A random sample of 100 observations from a normally distributed population possesses a mean equal to 83.2 and a standard deviation of 6.4. (pg. 323 #11)Construct and interpret a 95% confidence intervalConstruct and interpret a 99% confidence intervalIf you wish to estimate a population mean to within 0.2 with a 95% confidence interval and you know that variance is equal to 5.4, how many observations would you have to include in your sample? (pg. 349 #77)An estimate is needed of the average age of customers in a department store correct to within 2 years with probability .98. How many customers should be sampled? Assume the population standard deviation is 7.5.Patients who contract a rare disease have only a 2% chance of survival, but a new treatment is being tested throughout the country. A total of 800 patients have been treated and 35 have survived. Is the treatment effective? Use α = .005.Small bags of potato chips are labeled as containing “1 ounce” of chips. In order to determine whether the bagging machine is working properly, 50 bags of chips are selected from those about to be shipped and the contents of each bag is carefully determined. The sample mean is found to be 1.03 ounces, and the standard deviation is found to be .14 ounces.Is there sufficient evidence to conclude the bagging machine is not working properly (i.e. the mean is not 1 ounce)? Use α = .05.Find the p-value associated with this test.What is the Type I error in terms of this problem? What is the probability of a Type I error?The Type II error?A new pain reliever is claimed to bring relief in no more than 10 minutes. A random sample of 25 people is selected to take the new pain reliever and their mean time to relief is 10.8 minutes with a standard deviation of 3 minutes. Is there sufficient evidence to conclude the claim is false? Use α = .05.?Suppose we want to determine if there is a difference between the mean number of hours of study per week between athletes and non-athletes at UCF.??A random sample of 100 athletes and 500 non-athletes produced the results found below.Athletes??????????????????????????????Non-athletesMean = 22.6????????????Mean = 26.5StdDev = 4.3???????????????????????StdDev = 4.1n = 100?????????????????????????????????n = 500?a.?????Construct and interpret a 90% confidence interval for the difference in the mean number of hours.??b.?????Test if the data suggest at the 5% significance level that there is a difference in the mean number of hours of study per week between athletes and non-athletes at UCF.Re-do question # 33 if the sample sizes had been 20 athletes and 25 non-athletes. A speech pathologist wishes to see whether a new speaking program will reduce the number of pronunciation errors her students make when reading a set paragraph.?The number of errors before and after the program are shown below for a sample of 5 students.?Student??????????Errors?Before?????Errors After1??????????????????????????????????10????????????????????82??????????????????????????????????7??????????????????????43??????????????????????????????????9??????????????????????54??????????????????????????????????4??????????????????????35??????????????????????????????????8??????????????????????6?a.?????Construct and interpret a 99% confidence interval for the reduction in error.??b.?????Test if there is evidence to show the program reduces the mean number of errors.?Use =.01.? ?In a random sample of 250 persons who skipped breakfast, 102 reported that they experienced midmorning fatigue.??In a random sample of 250 persons who ate breakfast, 73 reported that they experienced midmorning fatigue.??a.??????????Construct and interpret a 95% confidence interval for the difference in midmorning fatigue.?b.??????????At the 0.01 level of significance, is midmorning fatigue more prevalent among persons who skipped breakfast?? ................
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