# Statistics Questions

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Statistics

Statistics78 The mean number of sick days an employee takes per year is believed to be about 10 Members of a personnel department do not believe this figure They randomly survey eight employees The number of sick days they took for the past year are as follows 12 4 15 3 11 8 6 8 Let x the number of sick days they took for the past year Should the personnel team believe that the mean number is 10

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Statistics77 An article in the San Jose Mercury News stated that students in th California state university system take 4 5 years on average to finish their undergraduate degrees Suppose you believe that the mean time is longer You conduct a survey of 49 students and obtain a sample mean of 5 1 with a sample standard deviation of 1 2 Do the data support your claim at the 1 percent level

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StatisticsA certain statistics instructor participates in triathlons The accompanying table lists times in minutes and seconds he recorded while riding a bicycle for five laps through each mile of a 3 mile loop Use a 0 05 significance level to test the claim that it takes the same time to ride each of the miles Does one of the miles appear to have a hill Click the icon to view the data table of the riding times Determine the null and alternative hypotheses Ho H Riding Times minutes and seconds Mile 1 Mile 2 Mile 3 3 15 3 23 3 24 3 21 3 22 3 19 3 18 3 23 3 22 3 18 3 35 3 31 3 29 3 32 3 30 0 Note when pasting the data into your technology each mile row will have separate columns for each minute and second entry You will need to convert each minute second entry into seconds only X nsl 9 3

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ProbabilitySuppose you model a game of chance with a discrete probability distribution Let X be the net amount o money won or lost by the player Let P X be the probability of the corresponding outcome The three events are as follows There is a 23 chance the player wins 3 dollars There is a 47 chance the player breaks even There is a 30 chance the player loses 6 dollars Complete the table below to model the scenario X P X

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ProbabilityMidsize Large and SUV with measured amounts of left leg femur force kN resul in the following Minitab display Using a 0 05 significance level test the claim that th four vehicle size categories have the same mean force on the femur of the left leg Does size of the car appear to have an effect on the force on the left femur in crash tests Analysis of Variance Source Size Error Total DF 3 52 55 Ho Adj SS 0 6381 20 4828 21 1209 Determine the null hypothesis H1 H2H3 H4 Adj MS 0 2127 0 3939 All of the means are different H H H H F Value 0 54 At least one of the means is different from the others P Value 0 657

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ProbabilityA data set includes the counts of chocolate chips from three different types of Chips Ahoy cookies The accompanying StatCrunch display shows results from analysis c variance used with those three types of cookies Use a 0 05 significance level to tes the claim that the three different types of cookies have the same mean number of chocolate chips ANOVA table Source DF Columns Error Total SS F Stat P value MS 886 9875 443 49375 57 7981 0 0001 Ho 2 77 590 83333 7 6731601 79 1477 8208 Determine the null hypothesis

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ProbabilityGiven the following Linear Regression model Pounds of Trash Per Household 1 5 x Person 1 5 How many pounds of trash are created by a household of 5 Edit View Insert Format Tools Table

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ProbabilityGiven the following Linear Regression model Pounds of Trash Per Household 1 5 x Person 1 5 What is the slope Edit View Insert Format Tools Table

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ProbabilityFind the standard deviation for the random variable X 5 3 7 9 14 P X x 0 23 0 23 0 24 0 15 0 15 X 6 165887121899 5 1248185333727 6 2192968252046 6 0422483398152

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ProbabilityWhich of the following is NOT true Choose the correct answer below CERED O A When testing for equality of three population means do not use multiple hypothesis tests with two samples at a time OB As the number of tests of significance increase the risk of finding a difference by chance alone increases OC If the decision from ANOVA is to reject the equality of the three population means the particular mean that differs from the others is kno OD The F test statistic is very sensitive to sample means even though it is obtained through two different estimates of the common population variar

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Probability0 2 0 3 0 1 0 35 0 05 2 6 7 10 13 Find the expected value of the above random variable

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StatisticsFind the expected value for the random variable X 3 1 7 11 13 P X x 0 14 0 22 0 17 0 24 0 23 8 07 04 6 4 6 62 3 63 3 98

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StatisticsX P x 0 0 2003 1 0 1503 0 0003 0 6491 2 3 Find the mean of this probability distribution Round your answer to 4 decimal p

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StatisticsX 0 1 2 3 P x 0 25 0 1 0 2 0 45 Find the standard deviation of this probability distribution Give your answer to 4 decim

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ProbabilityThe Insure com website reports that the mean annual premium for automobile insurance in the United States was 1 503 in March 2014 Being from Pennsylvania at that time you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of 1 430 with a standard deviation of s 160 a Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium O Hoi R 1 503 H 1 503 Ho 1 503 Ha 21 503 Ho 2 1 503 Ha 1 503 Hot S 1 503 H 1 503 Ho 1 503 H H 1 503 b What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean Use the mean annual premium in Pennsylvania minus the national mean c At a 0 05 test for a significant difference Find the value of the test statistic Round your answer to three decimal places Find the p value Round your answer to four decimal places p value State your conclusion O Reject Ho We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean O Do not reject Ho We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean O Reject Ho We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean Do not reject Ho We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean

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Statistics66 State the Type I and Type II errors in complete sentences given the following statements a The mean number of years Americans work before retiring is 34 b At most 60 percent of Americans vote in presidential elections The mean starting salary for San Jose State University graduates is at least 100 000 per year

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StatisticsYou may need to use the appropriate appendix table or technology to answer this question According to an article in Newsweek the natural ratio of girls to boys is 100 105 In China the birth ratio is 100 114 46 7 girls Suppose you don t believe the reported figures of the percent of girls born in China You conduct a study In this study you count the number of girls and boys born in 150 randomly chosen recent births There are 63 girls and 87 boys born of the 150 Based on your study do you believe that the percent of girls born in China is 46 7 Conduct a hypothesis test at the 5 level State the null and alternative hypotheses Enter for as needed Ho P 0 467 H P 0 467 What is the test statistic Round your answer to two decimal places 1 153 What is are the critical value s If using the z distribution round your answer s to two decimal places and if using the t distribution round your answer s to three decimal places Enter NONE for any unused answer blanks lower tail upper tail What is the decision of the test and what conclusions can be drawn At the 5 level of significance we would reject Ho and conclude that there is sufficient evidence to conclude that the percent of girls born in China is not equal to 46 7 O At the 5 level of significance we would reject Ho and conclude that there is not sufficient evidence to conclude that the percent of girls born in China is not equal to 46 7 At the 5 level of significance we would fail to reject Ho and conclude that there is not sufficient evidence to conclude that the percent of girls born in China is not equal to 46 7 O At the 5 level of significance we would fail to reject Ho and conclude that there is sufficient evidence to conclude that the percent of girls born in China is not equal to 46 7

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Statisticsmean work week has increased for Women at the 5 per 80 Your statistics instructor claims that 60 percent of the students who take her Elementary Statistics class go through life feeling more enriched For some reason that she can t quite figure out most people don t believe her You decide to check this out on your own You randomly survey 64 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class Now what do you think

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Statisticsmany hours per week they spend on the phone The sample mean was 4 75 hours with a sample standard deviation of 2 0 Conduct a hypothesis test The null and alternative hypotheses are as follows a Ho x 4 5 H x 4 5 b Ho uz 4 5 Hg 4 5 c Ho p 4 75 Ha p 4 75 d Ho p 4 5 H 4 5 9 2 Outcomes and the Type I and Type II Errors 66 State the Type I and Type Il errors in complete sentences given the following statements a The mean number of years Americans work before retiring is 34

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Statistics63 A recent survey of 273 randomly selected teens living in Massachusetts asked about social media Sixty three said that they routinely use a certain app to share pictures The researchers want to determine if there is good evidence that more than 30 percent of teens use this app The alternative hypothesis is as follows a p 0 30 b p 0 30 c p 0 30 d p 0 30 64 A statistics instructor believes that fewer than 20 percent of Evergreen Valley College EVC students attended the opening night midnight showing of the latest Harry Potter movie She surveys 84 of her students and finds that 11 attended the midnight showing An appropriate alternative hypothesis is as follows a p 0 20 b p 0 20 c p 0 20

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Statistics72 It is believed that Lake Tahoe Community College LTCC Intermediate Algebra students get seven hours of sleep per night on average A survey of 22 LTCC Intermediate Algebra students generated a mean of 7 24 hours with a standard deviation of 1 93 hours At a level of significance of 5 percent do LTCC Intermediate Algebra students get less than seven hours of sleep per night on average The distribution to be used for this test is X a N 7 24 1 93 22 h 724 193

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Probability69 A statistics instructor believes that fewer than 20 percent of Evergreen Valley College EVC students attended the opening midnight showing of the latest Harry Potter movie She surveys 84 of her students and finds that 11 of them attended the midnight showing The Type I error is to conclude that the percent of EVC students who attended is a at least 20 percent when in fact it is less than 20 percent b 20 percent when in fact it is 20 percent c less than 20 percent when in fact it is at least 20 percent d less than 20 percent when in fact it is less than 20 percent

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Statistics68 When a new drug is created the pharmaceutical company must subject it to testing before rec necessary permission from the U S Food and Drug Administration FDA to market the drug Suppose the null hypothesis is the drug is unsafe What is the Type II error a To conclude the drug is safe when in fact it is unsafe b Not to conclude the drug is safe when in fact it is safe c To conclude the drug is safe when in fact it is safe

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Statistics62 Some of the following statements refer to the null hypothesis some to the alternate hypothesis State the null hypothesis Ho and the alternative hypothesis Ha in terms of the appropriate parameter u or p

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Statisticsprincely salaries of his faculty He has talked with the football coach and the coach thinks that the llege is worried as always about having enough money to pay the Faber Aardvarks can win eight games this year Below are data on the number of games won and the total gate receipts for recent years as well as intermediate values Predict next year s gate if the Aardvarks win eight games Provide a complete interpretation of the results SHOW YOUR WORK 10 pts Year 2013 2012 2011 2010 2009 2008 Games Won 435869 10 Gate Receipts million 1 6 3 4 2 6 4 5 4 2 5 6

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StatisticsYou are investigating a complaint that the Yummy Junk Food Company s 10 ounce packages of barbecue flavored potato chips contain less than a full 10 ounces of the product You randomly sample and weigh 30 bags of the chips The mean of your sample is 9 82 and the unbiased estimate of the population standard deviation is 36 ounces Using an appropriate confidence interval determine whether or not there is reason to believe that the company is shorting its customers Provide a complete interpretation based on the evidence SHOW YOUR WORK 10 pts

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Statisticsidea she administers a different dose of caffeine to each of three groups of participants She then gives each group a short term memory test and counts the number of errors made by each A physiological psychologist suspects that caffeine affects short term memory In order to participant The data number of errors made by each participant and intermediate values are shown below Can the psychologist conclude that caffeine affects short term memory Provide a complete interpretation based on the evidence Graph the data if appropriate SHOW YOUR WORK 10 pts Control 0 mg 4 and its 4 orli sol sto 5 Low Dose 100 mg 523 High Dose 400 mg 11 12 10

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Statisticsall your work and provide complete interpretations Write the formula first plug in the values and then solve Please write legibly If you use additional paper number the pages and write your name on them 1 a A human resources worker has created a test of widget making skill and given it to a group of 5 job applicants The data are shown below Find the mean and standard deviation of this distribution SHOW YOUR WORK 6 pts Applicant 12345 Test Score 10 86758

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Statistics2 A psychologist wonders if it is true that red headed people have hotter tempers than people with other hair colors She administers a test that measures the tendency toward anger to a random sample of people with red hair and another random sample of people with other hair colors A higher score indicates a stronger tendency toward anger The scores and intermediate values are shown below Can the researcher conclude that red headed people have hotter tempers Provide a complete interpretation based on the evidence Graph the data if appropriate SHOW YOUR WORK 10 pts Red Heads 9 8 10 7 Others 3 4 3

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Statisticsd p 0 89 Recall the previously determined values po 0 85 and n 160 Now we are to find the test statistic for a new sample proportion p 0 89 Use these values to find the test statistic rounding the result to two decimal places Z p Po Po 1 PO n 0 89 0 85 1 42 0 85 1 0 85 160 1 42 0 85 Step 13 A lower tail test is being performed so the area to the left of the test statistic z 1 42 is needed Use the standard normal table to find the p value for this test statistic rounding the result to four decimal places p value

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StatisticsWhat is the relationship between the amount of time statistics students study per week and their final exam scores The results of the survey are shown below Time 16 7 3 6 15 10 10 5 87 78 57 Score 68 7 87 88 80 61 75 a Find the correlation coefficient r b The null and alternative hypotheses for correlation are Ho P 0 H pv 0 The p value is Round to 2 decimal places Round to four decimal places

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ProbabilityComplete the truth table for the given statement by filling in the required columns qvp pq TT TF FT F F q Complete the truth table qvp

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StatisticsConstruct a truth table for the given statement q p q Fill in the truth table PT T T q T F T q p q q p q

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ProbabilityThe circle graph shows the most important problems for the 19 175 341 high school teenagers in a country Without using a calculator estimate the number of high school teenagers for whom doing well in school is the most important problem Most Important Problems for High School Teenagers Doing Well in School 12 Social Pressures and Fitting in 21 OA 1 900 000 OB 5 700 000 OC 3 800 000 O D 7 600 000 Drugs 22 Others 29 Getting along with Parents 2 Getting into College 4 Sexual Issues 4 Crime and Violence in School 68 Doing well in school is the most important problem for approximately how many of the high school teenagers

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Probability4 Create a sample tree showing conditional probabilities for drawing 4 balls randomly out of a sock with 3 green and 7 yellow balls without replacement S JOLAS PASS

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StatisticsSuppose that you decide to buy a car for 27 635 including taxes and license fees You saved 8000 for a down payment and can get PA nt four year car loan at 7 52 Use PMT The monthly payment is Round to the nearest cent as needed The total interest for the loan is Round to the nearest cent as needed to find the monthly payment and the total interest for the loan

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Statisticsa Compute the value of the test statistic A sample of 58 items provided a mean of x 13 and a standard deviation of s 6 5 The hypotheses are given below Ho 14 Ha 14 A t test statistic will be used when the standard deviation is calculated from a sample instead of the population Recall that the test statistic t for a hypothesis is calculated as follows where x is the sample mean o is the hypothesized population mean s is the population standard deviation and n is the sample size X 40 S n The value for Ho is the hypothesized population mean we are testing for Here we have Submit t Skip you cannot come back There was a sample of 58 items given so we have n

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StatisticsNathan is investigating how long his phone s battery lasts in hours for various brightness levels on a scale of 0 100 His data is displayed in the table and graph below 20 9 2 Hours 7 6 Brightness Level x 27 O 45 69 71 72 80 Hours y 6 5 3 5 2 5 3 3 6 1 9 1 30 30 30 40 50 60 70 80 90 100 110 Brightness Level Calculate the correlation coefficient Round accurately to at least three decimals Use the correlation coefficient to describe the strength and direction

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StatisticsAidan is investigating how long his phone s battery lasts in hours for various brightness levels on a scale of 0 100 His data is displayed in the table and graph below 10 9 How s 8 7 6 5 4 3 2 1 Brightness Level x 22 23 24 31 37 50 77 96 Hours y 6 7 4 1 7 5 9 6 1 3 7 2 2 1 6 10 20 30 40 50 60 70 80 90 100 110 Brightness Level a Find the equation for the line of best fit Keep at least 3 decimals for each parameter in the equation You should begin by typing y

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StatisticsWhich scatter plot indicates a perfect positive correlation A D The graph B E shows a scatter plot with a perfect positive correlation C F

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ProbabilityStep 11 If the found p value is less than or equal to a given level of a then the null hypothesis will be rejected in favor of the alternative The p value was found to be 0 0384 and we are to compare the p value to a 0 05 Since the p value is less than or equal to is sufficient evidence to conclude that the population proportion is less than 0 85 p 0 85 Step 12 d p 0 89 Z Recall the previously determined values po 0 85 and n 160 Now we are to find the test statistic for a new sample proportion p 0 89 Use these values to find the test statistic rounding the result to two decimal places P Po Po 1 Po n 0 89 less than or equal to 0 05 the null hypothesis Hor will 0 85 10 85 160 will be rejected in favor of the alternative Therefore there is

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ProbabilityThe bar graph shows that life expectancy the number of years newborns are expected to live in a particular region has increased dramatically since ancient times Find the percent increase in average life expectancy of the region from the Stone Age to 2016 Round to the nearest integer as needed Average Life Expectancy years 80 70 60 50 40 30 20 10 0 27 29 32 34 52 63 72 Stone Ancient Middle 1900 1950 1980 2016 Greece Ages Age Time Period Year Q 17

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StatisticsHunter is investigating how long his phone s battery lasts in hours for various brightness levels on a scale of 0 100 His data is displayed in the table and graph below Brightness Level x Hours y 10 9 8 7 6 5 Hours A m 2 1 10 20 30 20 23 24 32 46 50 57 66 5 2 6 5 5 2 5 3 2 9 4 5 3 6 2 8 60 70 80 90 100 11 40 50 Brightness Level a Find the equation for the line of best fit Keep at least 4 decimals for each parameter in the equation

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ProbabilityA single die is rolled twice The 36 equally likely outcomes are shown to the right Find the probability of getting two numbers whose sum is 2 First Roll Second Roll 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 The probability of getting two numbers whose sum is 2 is Type an integer or a simplified fraction

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StatisticsA questionnaire was given to students The first question asked was How stressed have you been in the last week on a scale of 0 to 10 with 0 being not stressed at all and 10 being as stressed as possible The responses are shown in the table a Which stress rating describes the greatest number of students out of 10 Type a whole number b How many students responded with this rating students Type a whole number Stress Rating 0 1 2 3 4 5 6 7 8 9 10 Frequency 6 3 5 SHERHEE 17 18 13 14 28 31 17 17

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StatisticsA professor had students keep track of their social interactions for a week The number of social interactions over the week is shown in the following grouped frequency distribution How many students had at least 50 social interactions for the week The number of students was Type a whole number Number of Social Interactions 20 24 25 29 30 34 35 39 40 44 45 49 50 54 55 59 60 64 65 69 Frequency 14 10 15 11 72 17 12 3 2303 0

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StatisticsZ P Po Po 1 PO n 0 80 0 85 1 77 0 85 10 85 160 1 77 Step 10 A lower tail test is being performed so the area to the left of the test statistic z 1 77 is needed Use the standard normal table to find the p value for this test statistic rounding the result to four decimal places p value Enter a number 0 85 Submit Skip you cannot come back Need Help Read It

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ProbabilityFind a the mean b the deviation from the mean for each data item and c the sum of the deviations in part b for the following group of data items 57 67 62 57 72 a The mean is Simplify your answer b Complete the following table by entering the deviations for each data value 57 67 62 Simplify your answers c The sum of the deviations is Simplify your answer 57 72