manipulation influences other variables, the researcher is conducting a(n)

Transcription

1 Math 1342 Finals Review Selective Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) If a researcher manipulates one of the variables and tries to determine how the manipulation influences other variables, the researcher is conducting a(n) 2) In a true experimental study, the subjects should be assigned to groups randomly. If this is not possible and a researcher uses intact groups, they are performing a. 1) 2) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 3) A middle school student passes out leaflets to the adults at a school function. The leaflets ask the recipient to indicate whether they believe in anthropogenic global warming. The bottom of the leaflet indicates that the completed leaflet should be returned to the student. Identify the kind of sample that is being used. A) systematic sample B) cluster sample C) stratified sample D) sample of convenience 4) Determine which of the following describes quantitative data. i). the length of an object in feet ii). the speed of an object in meters per second iii). the number of objects that are blue A) iii only B) i and ii only C) i, ii, and iii D) i only 5) Determine which of the following describes qualitative data. i). the volume of a shipping container, in gallons ii). the name of the material from which the container is made iii). the shape of the container A) i and iii only B) i, ii, and iii C) ii and iii only D) i and ii only 3) 4) 5) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) What level of measurement allows for the ranking of data, a precise difference between units of measure, and also includes a true zero? 7) Give the boundaries of the given value. 8.6 millimeters 6) 7) 1

2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 8) An electronics manufacturer test every 200th cell phone to verify that it is functioning properly. Identify the kind of sample that is being used. A) simple random sample B) cluster sample C) stratified sample D) systematic sample 8) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 9) Which of the following best defines the relationship between confounding, dependent, and independent variables? 10) In which branch of statistics would a researcher acquire twenty-five 2000 Toyota Celicas, drive them until they had a major mechanical failure, record the final mileage, and then write a report for Car and Driver? 9) 10) 11) A recent statistics exam yielded the following 25 scores. Construct a grouped frequency 11) distribution with the class limits shown below Class Limits Tally Frequency

3 12) The following frequency distribution presents the weights in pounds (lb) of a sample of visitors to a health clinic. 12) Weight (lb) Frequency What is the class width? 13) State the reason why the following frequency distribution is incorrectly constructed. 13) Class Frequency ) State the reason why the following frequency distribution is incorrectly constructed. 14) Class Frequency ) Construct a frequency polygon from the following frequency distribution. Temperature Frequency ) 3

4 16) The following frequency distribution presents the weights in pounds (lb) of a sample of visitors to a health clinic. 16) Construct a frequency histogram. 17) One hundred students are shown an eight-digit number on a piece of cardboard 17) for three seconds and are asked to then recite the number from memory. The process is repeated until the student accurately recites the entire number from memory. The following histogram presents the number of trials it took each student to memorize the number. How many students memorized the number in three trials or less? 18) The scores on a recent statistics exam are shown below. Construct a stem and leaf plot 18) for the data. 98, 73, 64, 69, 86, 89, 77, 86, 91, 73 4

5 19) A student received the following grades last semester. Find the student's semester grade point average. 19) Course Credits Grade/Points Statistics 4 A / 4.0 Physics 5 F / 0.0 Sociology 3 B / 3.0 Literature 2 B / 3.0 Tennis 1 D / ) Find the mean, mode, median, and midrange for the following data set. 12, 15, 18, 18, 15, 22, 15, 30, 12 21) Following are heights, in inches, for a sample of college basketball players. 20) 21) Find the sample standard deviation for the heights of the basketball players. 22) A distribution in which approximately 68% of the data values fall within one standard deviation of the mean behaves according to 23) According to Chebyshev's theorem, the maximum proportion of data values from a data set that are more than 1.5 standard deviations from the mean is. 22) 23) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 24) A data set has a mean of 50 and a standard deviation of 10. Which of the following might possibly be true? A) No less than 30% of the data values are less than 30 or greater than 70. B) No more than 50% of the data values are between 30 and 70. C) At least 89% of the data values are between 20 and 80. D) At least 15% of the data values are less than 20 or greater than ) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 25) Check the following data set for outliers. 25) 73, 82, 84, 84, 86, 87, 89, 91 5

6 26) For the data set below, find the outlier(s). 26) 27) Indicate which student has the higher z score. 27) Art Major X = 46 X = 50.5 s = 5.2 Theater Major X = 70 X = 75.1 s = ) Construct a boxplot for the data set below. 28) Provide an appropriate response. 29) Use the ogive below to approximate the cumulative frequency for 24 hours. 29) 6

7 30) Use the ogive below to approximate the number in the sample. 30) 31) If a sportscaster makes an educated guess as to how well a team will do this season, he is using what type of probability? 32) The statement, "The probability that a certain sports team will win its next game is about 60%," is an example of 33) The arrow on the spinner shown below can be spun so that the arrowhead eventually stops in one of the three sectors labeled "A", "B", or "C". The spinner is spun 138 times and comes up "A" 55 times. Use the Empirical Rule to approximate the probability that the spinner comes up "A". 31) 32) 33) 34) A couple has four children. Find the probability that there is at least one girl. 34) 7

8 35) There are 28,524 undergraduate students enrolled at a certain university. The age distribution is as follows: 35) Age Range Number , , and up 6,401 Total 28,524 What is the probability that a student is between 23 and 30 years old? Odds are used in gambling games to make them fair. For example, if you rolled a die and won every time you rolled a 6, then you would win on average once every 6 times. So that the game is fair, the odds of 5 to 1 are given. This means that if you bet $1 and won, you could win $5. On average, you would win $5 once in six rolls and lose $1 on the other five rolls - hence the term fair game. In most gambling games, the odds given are not fair. For example, if the odds of winning are really 20 to 1, the ho might offer 15 to 1 in order to make a profit. Odds can be expressed as a fraction or as a ratio, such as 1, 5:1, or 5 to 1. Odds are computed in favor of the eve 5 against the event. The formulas for odds are Odds in favor = P(E) 1 - P(E) Odds against = P(E) 1 - P(E) In the die example, Odds in favor of a 6 = = 1 5 or 1:5 Odds against a 6 = = 5 1 or 5:1 36) Find the odds for and against rolling a die and getting a 4. 36) 8

9 37) On a recent Saturday, a total of 1,071 people visited a local library. Of these people, 245 were under age 10, 496 were aged 10 18, 179 were aged 19 30, and the rest were more than 30 years old. 37) One person is sampled at random. What is the probability that the person is less than 19 years old? 38) According to popular belief, 80% of adults enjoy drinking beer. Choose a group of 2 adults at random. The probability that all of them enjoy drinking beer is: 39) In a second grade class containing 14 girls and 8 boys, 2 students are selected at random to give out the math papers. What is the probability that the second student chosen is a boy, given that the first one was a girl? 40) How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a row at the opera if Andy and Betty must sit together? 41) In a company there are 8 executives: 6 women and 2 men. 2 are selected to attend a management seminar. Find the probability that 1 men and 1 woman will be selected. 42) Determine whether the table represents a discrete probability distribution. 38) 39) 40) 41) 42) x P(x) ) Construct the probability distribution for the number of heads obtained when tossing four coins. Draw a graph of the distribution. 44) What is the standard deviation of the following probability distribution. 43) 44) X P(X)

10 45) A landscape contractor bids on jobs where he can make $2,700 profit. The probabilities of getting 1, 2, 3, or 4 jobs per month are shown. 45) Number of Jobs Probability Find the contractor s expected profit per month. 46) Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 8, p = 0.5, P(6 or more) 46) 47) The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 18 adult dogs is studied. What is the standard deviation of the number of dogs who weigh 65 lb or more? 48) Use the multinomial formula and find the probability for the following data. n =8, X 1 = 4, X 2 = 3, X 3 = 1, p 1 = 0.30, p 2 = 0.50, p 3 = ) 48) 49) If there are 20 typographical errors randomly distributed in a 250-page document, find the probability that a given page contains exactly two errors. 50) What is the area under the standard normal distribution curve between z = 1.50 and z = 2.50? 49) 50) 10

11 51) Find the area under the standard normal distribution curve to the left of z = ) 52) The average gas mileage of a certain model car is 30.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.75 miles per gallon, find the probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon. 53) The average height of flowering cherry trees in a certain nursery is 9.5 feet. If the heights are normally distributed with a standard deviation of 1.3 feet, find the probability that a tree is less than 11.5 feet tall. 54) The average charitable contribution itemized per income tax return in Pennsylvania is $792. Suppose that the distribution of contributions is normal with a standard deviation of $103. Find the limits for the middle 50% of contributions. 55) A sample of size 95 will be drawn from a population with mean 25 and standard deviation 13. Find the probability that x will be between 22 and ) 53) 54) 55) 56) Use the normal approximation to find the indicated probability. The sample size 56) is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 96, p = 0.36: P(29 X 43) 57) In a recent year, about 26% of Americans 18 and older are single. What is the probability that in a random sample of 180 Americans 18 or older more than 28 are single? 57) Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution. 58) The amounts of time employees of a telecommunications company have worked for the 58) company are normally distributed with a mean of 5.1 years and a standard deviation of 2.0 years. Random samples of size 18 are drawn from the population and the mean of each sample is determined. 11

12 Provide an appropriate response. 59) What happens to the mean and standard deviation of the distribution of sample means as the size of the sample decreases? 59) 60) A sample of size n = 10 is drawn from an approximately normal population whose standard deviation is = The sample mean is x = Construct a 99% confidence interval for. 61) A study of peach trees found that the average number of peaches per tree was 525. The standard deviation of the population is 140 peaches per tree. A scientist wishes to find the 90% confidence interval for the mean number of peaches per tree. How many trees does she need to sample to obtain an average accurate to within 18 peaches per tree? 62) A random sample of magnesium concentrations (in parts per million, or ppm) in ground water from various locations follows. Estimate the mean concentration of magnesium in ppm with 90% confidence. Assume = ) 61) 62) 63) A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz. and the sample standard deviation is 0.70 oz., find the 95% confidence interval of the true mean. 63) 64) A state representative wishes to estimate the mean number of women representatives per state legislature. A random sample of 17 states is selected, and the number of women representatives is shown. Based on the sample, what is the point estimate of the mean? Find the 90% confidence interval of the mean population. (Note : The population mean is actually 32.2.) ) 65) Find the critical value t /2 needed to construct a confidence interval of the given level with the given sample size. Level 95%, sample size 8 65) 12

13 66) Use the given data to construct a confidence interval of the requested level. x = 80, n = 198, confidence level 99% 67) A recent poll of 700 people who work indoors found that 278 smoke. If the researchers want to be 98% confident of their results to within 3.5 percentage points, how large a sample is necessary? 68) What is the 95% confidence interval for the standard deviation of birth weights at County General Hospital, if the standard deviation of the last 25 babies born there was 1.1 pounds? 69) What is the 90% confidence interval for the variance of exam scores for 28 algebra students, if the standard deviation of their last exam was 12.7? 70) A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 25.7 miles per gallon (mpg). A random sample of 42 cars are selected and the air filter of each is replaced with a new one. Let be the population mean fuel efficiency score that would occur if every car's air filter were replaced. The air filter change is deemed effective if > 25.7 mpg. A test is made of H 0 : = 25.7 versus H 1 : > ) 67) 68) 69) 70) Assume that the air filter changes are effective. Which type of error is impossible? 71) Determine whether the outcome is a Type I error, a Type II error, or a correct decision. 71) A test is made of H 0 : = 13 versus H 1 : 13. The true value of is 12 and H 0 is not rejected. 72) Determine whether the alternative hypothesis is left-tailed, right-tailed, or two-tailed. 72) H 0 : = 44 H 1 : > 44 73) Using the z table, find the critical value (or values) for an = 0.09 two-tailed test. 73) 74) A grocery store owner claims that the mean amount spent per checkout is more than $73. A test is made of H 0 : = 73 versus H 1 : > 73. The null hypothesis is rejected. State the appropriate conclusion. 75) A test is made of H 0 : = 67 versus H 1 : 67. A sample of size n = 63 is drawn, and x = 64. The population standard deviation is = 27. Compute the value of the test statistic z. 74) 75) 13

14 Provide an appropriate response. 76) Given Ha: µ > 85 and P = Do you reject or fail to reject H0 at the 0.01 level of significance? 76) 77) According to Beautiful Bride magazine, the average age of a groom is now 26.2 years. A sample of 16 prospective grooms in Chicago revealed that their average age was 26.6 years with a standard deviation of 5.3 years. What is the test value for a t test of the claim? 77) 78) In a simple random sample of size 62, there were 22 individuals in the category of interest. It is desired to test H 0 : p = 0.36 versus H 1 : p < Compute the test statistic z. 79) If the test value for the difference between the means of two large samples is 2.57 when the critical value is 1.96, what decision should be made? 78) 79) 80) A sociologist expects the life expectancy of people in Africa is different than the life expectancy of people in Asia. The data obtained is shown in the table below. Determine the 95% confidence interval for the difference in the population means. 80) Africa X 1 = 55.3 yr. 1 = 8.1 yr. Asia X 2 = 65.2 yr. 2 = 9.3 yr. n 1 = 53 n 2 = 42 81) A health care company reported that an insured woman spends on average 2.5 days in the hospital for a routine childbirth, while an uninsured woman spends on average 1.6 days. Assume two random samples of 16 women each were used in both samples. The standard deviation of the first sample is equal to 0.6 day, and the standard deviation of the second sample is 0.2 day. Find the 99% confidence interval for the differences of the means. 81) 14

15 82) Which of the following would be classified as dependent samples? 82) I Weights of identical twins Effects of a drug on tumor size of two different groups of people, measured by a II before-and-after test III The effectiveness of two different brands of antacid on two different groups of people The effectiveness of two different training programs on two different groups of IV individuals V Test scores of the same students in statistics and art 83) Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 15 of 42 at one school and 22 of 40 at the other have ear infections. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools? 84) What is the critical value for a two-tailed F test with = 0.10, when the sample size from which the variance for the numerator was obtained is 10, and the sample size from which the denominator was obtained is 24? 83) 84) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 85) Using Table H, find the critical value. Sample 1: s 2 1 = 158, n 1 = 25 85) Sample 1: s 2 1 = 130, n 1 = 14 Two-tailed = 0.05 A) 2.79 B) 2.89 C) 2.35 D) ) Determine the type of relationship shown in the figure below. 86) A) There is no relationship. B) negative C) multiple D) positive 15

16 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 87) An experiment is carried out to determine the relationship between the average speed (rpm) and power (hp) of a mixer. Draw the scatter plot for the variables. Average Speed Power ) 88) The equation of a regression line is y = x. What is the intercept of this line? 88) 89) If the correlation coefficient is 0.790, what is the explained variation? 89) 90) If the correlation coefficient is 0.930, what is the unexplained variation? 90) 16

17 Answer Key Testname: MATH 1342 FINALS REVIEW S_SA 1) experimental study. 2) quasi-experimental study 3) D 4) C 5) C 6) ratio 7) millimeters 8) D 9) The confounding variable influences the dependent variable, but is not separated from the independent variable. 10) descriptive statistics 11) Class Limits Frequency ) 10 13) class width is not uniform 14) a class has been omitted 15) 17

18 Answer Key Testname: MATH 1342 FINALS REVIEW S_SA 16) 17) 13 18) ) ) mean = 17.4 mode = 15 median = 15 midrange = ) ) the empirical rule. 23) ) C 25) 73 is an outlier 26) 123 and ) The theater major has a higher score than the art major. 28) 29) 63 30) 80 31) subjective probability 32) subjective probability. 33)

19 Answer Key Testname: MATH 1342 FINALS REVIEW S_SA 34) ) ) 1:5, 5:1 37) ) ) 21 40) 12 41) ) No 43) Number of Heads X Probability P(X) ) ) $7,560 46) ) ) ) ) ) ) ) ) $723 and $861 55) ) ) ) 5.1 years, 0.47 years 19

20 Answer Key Testname: MATH 1342 FINALS REVIEW S_SA 59) The mean of the sample means stays constant and the standard error increases. 60) < < ) ) 61.5 < < ) 14.6 < < ) Point Estimate : 33.8 CI : < < ) ) < p < ) ) 0.9 < < ) < 2 < ) Type I 71) Type II error 72) right-tailed 73) ± ) The mean checkout amount is greater than $73. 75) ) reject H0 77) ) ) Reject the null hypothesis. 80) < 1-2 < ) 0.4 < 1-2 < ) I, II, V 83) No, because the test value is inside the noncritical region < z < ) ) B 86) D 20

21 Answer Key Testname: MATH 1342 FINALS REVIEW S_SA 87) 88) ) 62.4% 90) 13.5% 21