Statistics Final exam study

#20 A simple random sample of size n equals 350 individuals who are currently employed is asked if they work at home at least once per week. Of the 350 employed individuals​ surveyed, 43 responded that they did work at home at least once per week. Construct a​ 99% confidence interval for the population proportion of employed individuals who work at home at least once per week. The lower bound is The upper bound is

Go to statcrunch-stat-proportion stat-one sample summary. n=350 successes=43 0.99 confidence level The lower bound is 0.078 The upper bound is 0.168

#18 (a)(b) An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weights of various cars and their gas mileages. a) Determine which variable is the explanatory variable and which is the response variable. b) Draw a scatter diagram of the data. Choose the correct scatter plot

a)The explanatory variable is the weight and the response variable is the miles per gallon b) Draw a scatter plot. Go to graphs-scatter plot-x=weight y=mph. B is the answer. See picture.

#24 A ___________ ____________is the value of a statistic that estimates the value of a parameter.

point estimate

#17 Which measure of central tendency may not exist for all numeric data​ sets?

Mode

a) 1/17 b) 16/17 c) 5/17 d) 9/17

#1 A fair 17-sided die is rolled. ​(a) What is the probability of rolling a​ 7? ​(b) What is the probability of not rolling a​ 7? ​(c) What is the probability of rolling a number greater than​ 12? ​(d) What is the probability of rolling an even number or a​ 5?

#12 Identify the type of sampling used. ​Thirty-five math​ majors, 40 music​ majors, and 61 history majors are randomly selected from 537 math​ majors, 273 music​ majors, and 379 history majors at the state university. What sampling technique is​ used?

stratified

#15 Suppose the list below shows how many text messages Elyse sent each day for the last 10 days. If Elyse wants to know how many text messges she typically sends each​ day, which measure of central tendency better describes the typical number of text messages per​ day? 21 22 24 26 26 29 32 32 33 88

Go to statcrunch. Type numbers in. Go to summary-stat. Choose the column1 then choose median and mean. Calculate: Mean=33.3, Median=27.5 Which measure of central tendency better describes the typical number of text messages per day? Median; The median of 27.5 is a better representative of the center since it is resistant to the one extreme value. The mean of 33.3 is not representative of the typical number of texts since only one number is larger than the mean.

#11 Determine the level of measurement of the variable. Number of text messages sent in a month.

ratio

A license plate consists of 3 letters: KLM and 26 letters and 0-9 numbers. So 3 x 25 x 24 x 10 x 9 x 8 = 1,296,000

#3 A license plate is to consist of 3 letters followed by 3 digits. Determine the number of different license plates possible if the first letter must be an​ K, L, or M and repetition of letters and numbers is not permitted.

#16. In​ Marissa's calculus​ course, attendance counts for 15​% of the​ grade, quizzes count for 10​% of the​ grade, exams count for 50​% of the​ grade, and the final exam counts for 25​% of the grade. Marissa had a 100​% average for​ attendance, 89​% for​ quizzes, 82​% for​ exams, and 85​% on the final. Determine​ Marissa's course average.

1.0 x 15 (attendance) + 89 x 0.10(Quizzes) + 82 x 0.50 (exams) +.85 x 0.25(final) =86.15

#8 Find the value of za z0.49

Answer = 0.03. Change the negative to a positive and round two decimal places.

#25 Compute the critical value za/2 that corresponds to a 98% level of confidence za/2=

To solve go to normal calculator between. Insert p( <x<=0.98. Answer is 0.233

#13 An airline offers discounted flights from Atlanta to five American cities. Below is a frequency distribution of the number of tickets purchased for each location over a​ two-month period. a) Construct a relative frequency distribution of the data (b) What proportion of the tickets were for New​ York?

To solve total all the frequencies. The total is 4260. To solve the relative frequency for Las Vegas take 1159/4260=0.272 and so on. For (b) look at the relative frequency of New York. Answer: 0.338 See picture

#23 If we reject the null hypothesis when the statement in the null hypothesis is​ true, we have made a Type​ _______ error.

Type 1 error

#22 Fill in the blanks to complete the statement. The​ _______ _______ is a statement we are trying to find evidence to support

alternative hypothesis

#21 The shape of the distribution of the time required to get an oil change at a 15​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 16.2 minutes​, and the standard deviation is 3.4 minutes. What is the probability that a random sample of n=45 oil changes results in a sample mean time less than 15 ​minutes?

μ = 16.2, std=3.4 Sample μ = 16.2 Calculate sample std=3.4/sq. rt of 45=0.5067 Go to statcrunch-normal calculator. See picture. Though the answer is 0.0089 round to 0.0090

a) p(mn) = (0.17) (0.17) (0.17) (0.17) (0.17) (0.17) =0.000024 b) What is the probabillity that among the four randomly selected 18 to 25 year olds at least one is a marijuana user? 1-0.83^6= 1-0.32694= 0.67306

#2 According to the Statistical Abstract of the United States​, about​ 17% of all​ 18- to​ 25-year-olds are current marijuana users. ​(a) What is the probability that six randomly selected​ 18- to​ 25-year-olds are all marijuana​ users? ​(b) What is the probability that among six randomly selected​ 18- to​ 25-year-olds at least one is a marijuana​ user?

Go to calculator. nCr because order doesn't matter. 60Cr8=2,558,620,845

#4 How many different simple random samples of size 8 can be obtained from a population whose size is 60?

a) c b) 1.6

#5 In the following probability​ distribution, the random variable X represents the number of activities a parent of a 6th dash to 8th grade student is involved in. a) Draw a probability histogram. Choose the one below.

#19 Explain the meaning of the following percentiles in parts​ (a) and​ (b). ​(a) The 10th percentile of the weight of males 36 months of age in a certain city is 12.0 kg. ​(b) The 90th percentile of the length of newborn females in a certain city is 54.3 cm.

(a) Choose the correct answer 10​% of​ 36-month-old males weigh 12.0 kg or​ less, and 90​% of​ 36-month-old males weigh more than 12.0 kg (b) 90​% of newborn females have a length of 54.3 cm or​ less, and 10​% of newborn females have a length that is more than 54.3 cm.

b) 1.6, a c) 1.4 d) 0.268 Use custom calculator to calculate since there is not a complete data set. d= 0.116 + 0.152= 0.268

5# (b.) Compute and interpret the mean of the random variable X The mean= Which of the following interpretations of the mean is​ correct? A. As the number of experiments n​ increases, the mean of the observations will approach the mean of the random variable. B. The observed value of the random variable will be equal to the mean of the random variable in most experiments. C. As the number of experiments n​ decreases, the mean of the observations will approach the mean of the random variable. D.The observed value of the random variable will be less than the mean of the random variable in most experiments. (c) ) Compute the standard deviation of the random variable X. The standard deviation is ________activities. (d) What is the probability that a randomly selected student has a parent involved in three or four​ activities? The probability is _________________ .

#6 Suppose that a recent poll found that 40% of adults in a certain country believe that the overall state of moral values is poor. A survey of a random sample of 60 adults in this country is conducted in which they are asked to disclose their feelings on the overall state of moral values. a) Find and interpret the probability that exactly 26 of those surveyed feel the state of morals is poor. The probability that exactly 26 of those surveyed feel the state of morals is poor is _________________________ Interpret the results. Choose the correct answer below. A. In 100​ trials, we expect about 20 trials to result in exactly 26 adults who feel the state of morals is poor. B. In 100​ trials, we expect about 9 trials to result in exactly 26 adults who feel the state of morals is poor. C. In 100​ trials, we expect about 16 trials to result in exactly 26 adults who feel the state of morals is poor. D. In 100​ trials, we expect about 14 trials to result in exactly 26 adults who feel the state of morals is poor. b) Find the probability that no more than 21 of those surveyed feel that state of morals is poor. The probability that no more than 21 of those surveyed feel that state of morals is poor is ________________ (c) Find the probability that more than 16 of those surveyed feel the state of morals is poor. The probability that more than 16 of those surveyed feel the state of morals is poor is _____________________ (d) Find the probability that 18 or 19 believe the state of morals is poor. The probability that 18 or 19 believe the state of morals is poor is_________________.

Answer a) 0.0902 solved with binomial calculator. See picture. B (b) 0.2568 (c) 0.9779 (d) 0.0757

#7 A quiz consists of 100 multiple choice​ questions, each with five possible​ answers, only one of which is correct. If a student guesses on each​ question, what is the mean and standard deviation of the number of correct​ answers? Round to the nearest thousandth. A. The mean is 50. The standard deviation is 7.071. B. The mean is 20. The standard deviation is 4.472. C. The mean is 50. The standard deviation is 4. D. The mean is 20. The standard deviation is 4.

The mean is 20. The standard deviation is 4. See picture for solution.

#14 The data below represent the per capita​ (average) disposable income​ (income after​ taxes) for 25 randomly selected cities in a recent year. Complete parts​ (a) through​ c 30,120 34,234 36,947 40,230 30,427 34,614 37,375 41,105 30,757 34,960 37,829 41,419 32,104 35,105 38,344 52,405 33,007 35,538 38,607 33,728 35,817 38,856 33,982 36,028 39709 a) Construct a frequency distribution with the first class having a lower class limit of​ 30,000 and a class width of 6000. (b) Construct a frequency histogram of the data. Choose the correct graph below. (c) Describe the shape of the distribution.

To solve (a) go to statcrunch-bin column-select column-30,000 for lower class limit and 6000 for class width. Then go to stat-tables-select columns-bin(var1) select statistics frequency. When you enter the classes; however, be sure to go 30,000-35,999; 36,000-41,999; 42,000-47,999; and 48,000-53,999. The table you calculated will give you the frequencies of 13, 11, and 1. It will omit the frequency for 42,000-47,999 because is 0, but include it anyway. (b) See picture (c) skewed right

#10 A community college employs 158​ full-time faculty members. To gain the​ faculty's opinions about upcoming contract​ negotiations, the president of the faculty union wishes to obtain a simple random sample that will consist of 5 faculty members. She numbers the faculty 1 to 158. Use StatCrunch to obtain a simple random sample of five faculty members using a fixed seed of 31.

To solve go to statcrunch. Then go to data-simulate-discrete uniform. Then rows-5-columns 1. Then discrete uniform parameters minimun-1-maximum-158. Under Seedling select use fixed seed. Put in 31. Calculate. Pull from column from top down. See answer in picture.

n 2004​, 22​% of university undergraduate students had at least one tattoo. A health practitioner obtains a random sample of 1039 university undergraduates and finds that 223 have at least one tattoo. Has the proportion of university undergraduate students with at least one tattoo changed since 2004​? Use the alpha=0.01 level of significance. Complete parts ​(a) through ​(d) below. a) Determine the alternate hypothesis H0: p HA: p b) p value = c) state the conclusion for test d) state the conclusion in context of the problem

a) Determine the alternate hypothesis H0: p = 0.22 HA: p ≠ 0.22 b) Calculate by going to statcrunch-One sample proportion summary hypothesis test P value =0.676 c) State the conclusion for the test. Do not reject H0 because the​ P-value is greater than the a=0.01 level of significance. d) State conclusion in context of problem There is not sufficient evidence at the alphaequals0.01 level of significance to conclude that the proportion of university undergraduate students with at least one tattoo changed since 2004.

#18 (c)(d) An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weights of various cars and their gas mileages. (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon. (d) Does a linear relation exist between the weight of a car and its miles per gallon in the​ city?

c) Go to statcrunch-stat-regression x variable: weight y variable: mph then calculate. Under the table look at Simple linear results. See R (correlation coefficient) = -0.95882201 r=-959 d) There appears to be a negative linear association because r is negative and less than the negative critical value.

#9 This is a bonus question worth 5 points. If​ correct, I will adjust your score after your test is completed. The following is article by The Associated Press​ (AP), Washington, published on February​ 25, 2012. ​"President Barack Obama says​ there's no​ "silver bullet" to pierce the heart of rising gasoline prices. In his weekly radio and Internet​ address, he dismisses Republican plans to address the problem as little more than gimmicks. He says the main GOP answer is drilling and adds​ that's already happening. Obama says U.S. dependence on foreign oil​ can't be reduced overnight and that an​ "all of the​ above" approach is needed to maximize limited resources and develop new ones. For the​ GOP, Texas Sen. Kay Bailey Hutchison puts the blame for the price spike squarely on the Obama administration. She says​ he's blocked potential new sources of oil and gas. Economists say​ there's not much a president of either party can do about gasoline prices in the short term. An Associated Press poll says 7 in 10 Americans find the issue​ [gasoline prices] deeply​ important." Based on the information in the​ article, you decide to conduct a survey of 20 students and ask one​ queston: "Do you find the issue of gasoline prices deeply​ important?". What is the probability that half of the students answer​ "Yes" to this​ question?

p=0.7 n= 20 p(x =10 to represent half the students who say yes. Solve on binomial calculator see picture. Probability half the students say yes is 0.0308.