Statistics Questions

Find 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

X 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

X 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

The 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

66 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

You 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

mean 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

many 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

63 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

72 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

Write 2 002 10 9 in standard notation

69 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

68 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

62 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

princely 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

You 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

idea 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

all 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

2 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

d 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

What 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

Complete 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

Construct 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

The 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

4 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

Suppose 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

a 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

Nathan 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

Aidan 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

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

Step 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

The 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

Hunter 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

A 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

A 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

A 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

Z 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

Find 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

21 A day of the week is to be chosen at random from the 7 day week Let event A be that a day from the 5 day work week was chosen Let event B be that the day of the week chosen starts with the letters S or T Find P A and P B Are events A and B mutually exclusive Why

The time required to assemble a single Play Station 5 is approximately normally distributed with 15 44 minutes and o 1 2 minutes A random sample of 19 Play Station 5 assembly times is selected Find the minimum assembly time of the upper 10 of average assembly times Round to at least 2 decimal places if needed

NOTE This problem has many steps You are asked to enter intermediate values in the process These answers will require a fixed number of decimal points However you MUST ALWAYS REMEMBER that you are not using the rounded numbers in your future calculations The only exception to this is that you may use z scores rounded to three decimal places of course you also may use the unrounded version as well In a certain school district in a large metropolitan area the SAT scores over that past five years are normally distributed with a mean of 1458 Furthermore P10 is 1065 For a normal distribution what is the z score for the 10 th percentile z Enter answer rounded to three decimal places Using this information what is the standard deviation of this population of SAT scores sigma Enter answer rounded to the nearest whole number For a normal distribution what is the z score for the 99 th percentile Z Enter answer rounded to three decimal places Now use all of the information to determine what the P99 score is for this population P99

The Acme Company manufactures widgets The distribution of widget weights is bell shaped The widget weights have a mean of 45 ounces and a standard deviation of 7 ounces Use the Standard Deviation Rule also known as the Empirical Rule Suggestion sketch the distribution in order to answer these questions a 68 of the widget weights lie between and b What percentage of the widget weights lie between 24 and 52 ounces c What percentage of the widget weights lie below 59 6

The actual volumes of quart size jars of Hellmann s mayonnaise are uniformly distributed from 31 46 to 32 59 fluid ounces Find the average volume of a quart size jar of Hellmann s in fluid ounces NOTE There are 32 fluid ounces in a quart O 32 059 O 32 138 O 31 912 O 31 991 O 31 946 32 104 32 025

The values of a particular distribution are uniformly distributed between 3 and 7 Write answer as a fraction or as a decimal rounded to at least 2 places 2 DIE 3 5 6 7

Consider the density curve plotted below PDF X 0 275 0 25 0 225 Q3 0 2 IQR 0 175 0 15 0 125 0 1 0 075 0 05 0 025 Find P X 18 Find P X 19 15 Calculate the following Q1 median 16 17 Density Curve 18 X 9 20 a

The following table is for all pets in the village of MakeBelieve Age 7 years Age 7 years Totals Dogs Cats Totals In Make Believe the probability the age of a pet more than 7 years old is 0 4 for a dog and 0 6 for a cat Complete the table Compute the probability that the pet is a cat given it is not more than 7 years old

20 points A basketball player has a 62 chance of making each free throw What is the probability that the player makes exactly four out of six free throws 32 1 86 66

A class has 20 students What is the probability that at least 5 students were born on a weekend 45 82 72

The following table is similar to the table that appears in Example 12 4 The What You Know information has been provided Complete the table by filling in the How You Know It column What You Know The sampling distribution of x is centered at the actual but unknown value of the population mean An estimate of the standard deviation of x which describes how the x values spread out around the population mean is 0 24 0 0 X X H Hl X 1 3 9 x 30 H 00 1 3 29 Of X 29 1 3 30 1 3 29 1 3 How You Know It

Suppose an article describes results from a representative sample of American adults in 2018 and an independently selected representative sample of American adults taken in 2019 Survey participants were asked the following question If you could live anywhere you wished where would you prefer to live in a big city small city suburb of a big city suburb of a small city or in a town or rural area In 2018 394 of the 1 000 people surveyed selected town or rural area In 2019 489 of the 1 000 people surveyed selected town or rural area Use a significance level of 0 01 to determine if there is convincing evidence that the proportion of all American adults who prefer to live in a rural area increased from 2018 to 2019 Let p be the population proportion of American adults in 2018 who prefer to live in a rural area and p be the population proportion of American adults in 2019 who prefer to live in a rural area LAUSE SALT State the appropriate null and alternative hypotheses Enter for as needed Ho H Find the test statistic Round your answer to two decimal places MY NOTES Use technology to find the P value Round your answer to four decimal places P value State your conclusion Fail to reject Ho We have convincing evidence that the proportion of all American adults who prefer to live in a rural area increased from 2018 to 2019 Reject Ho We do not have convincing evidence that the proportion of all American adults who prefer to live in a rural area increased from 2018 to 2019 Fail to reject Ho We do not have convincing evidence that the proportion of all American adults who prefer to live in a rural area increased from 2018 to 2019 Reject Ho We have convincing evidence that the proportion of all American adults who prefer to live in a rural area increased from 2018 to 2019