Statistics Questions

12 y 3x 5 Which of the following scenarios could be described by the equation above A The number of cards Larry has if he had 3 collector cards and he adds 5 more cards to his collection every 3 days The distance of a tortoise from the starting line in a race if the tortoise started 5 miles ahead of the starting line and moved at a pace of 3 miles per hour B The number of points earned on a test if each question is worth 5 points and Mr Felder subtracted 3 points for every incorrect answer D The amount of money Miranda has if for every 5 Miranda earns she gives 3 to her mother

15 Write in slope intercept form an equation of the line that passes through the given points 4 1 8 2

22 Directions 21 3 Graph the following slope intercept equation 2 CLICK TO SELECT LINE AB 6 5 32 2 1 30 1

4 Change z 2y 4 into slope intercept for N N N NI le 1 NIN

23 Write the given equation in slope intercept form Given 3x 2y 10 A y x 5 B y C y D y 3232 SHOW HINT 3232 5 x 5 x 5

CK TO SELECT LINE AA to 1 S 4 B 2 M 100 CV 4 2 3 4 5 10 6 7 8 9

A line has a slope of 3 and passes through the point 5 4 7 Find the equation of the line Ay 3x 19 y 3x 19 y 3x 19 y 3x 19

21 Consider the graph below in 3 2 O 2 3 B The equation of the line is 5 6 2 What is the equation of the line in slope intercept form

18 Convert the equation standard form equation into Slope intercept form rewrite it as y mz b Standard form 4y 3x 16 Slope intercept form

Graph the following standard form equation y 3 CLICK TO SELECT UNE AA 14 6 4 92 ey 24 5 4 3 N H 201 H N 3 A

5 A lab wants to compare the results for two separate weight loss programs Compute the test statistic given that a random sample of 54 dieters on Program 1 lost an average of 9 3 pounds with a population standard deviation of 3 1 pounds and a random sample of 48 dieters on Program 2 lost and average of 7 9 pounds with a population standard deviation of 2 8 pounds Test at the 95 confidence level x 0 05 whether there s a difference in the pounds lost between the two diets The null and alternative hypotheses a Compute the test statistic z score Ho M b What is the p value for the test statistic HA M1 M

Identify the type I error and the type II error that corresponds to the given hypothesis The proportion of people who write with their left hand is equal to 0 19 Which of the following is a type I error A Fail to reject the claim that the proportion of people who write with their left hand is 0 19 when the proportion is actually different from 0 19 B Reject the claim that the proportion of people who write with their left hand is 0 19 when the proportion is actually different from 0 19 OC Reject the claim that the proportion of people who write with their left hand is 0 19 when the proportion is actually 0 19 OD Fail to reject the claim that the proportion of people who write with their left hand is 0 19 when the proportion is actually 0 19

Claim The mean systolic blood pressure of all healthy adults is less than than 119 mm Hg Sample data For 260 healthy adults the meam systolic blood pressure level is 118 77 mm Hg and the standard deviation is 15 72 mm Hg The null and alternative hypotheses are Ho H 119 and H 119 Find the value of the test statistic The value of the test statistic is Round to two decimal places as needed

Claim The mean systolic blood pressure of all healthy adults is less than 123 mm Hg Sample data For 254 healthy adults the mean systolic blood pressure level is 122 74 mm Hg and the standard deviation is 16 18 mm Hg Complete parts a and b a Express the original claim in symbolic form Let the parameter represent a value with respect to systolic blood pressure of a healthy adult Type an integer or a decimal Do not round

Claim Fewer than 10 3 of homes have only a landline telephone and no wireless phone Sample data A survey by the National Cente for Health Statistics showed that among 15 937 homes 5 81 had landline phones without wireless phones Complete parts a and b a Express the original claim in symbolic form Let the parameter represent a value with respect to homes that have only a landline telephone and no wireless phone Type an integer or a decimal Do not round

The test statistic of z 1 86 is obtained when testing the claim that p 0 355 a Identify the hypothesis test as being two tailed left tailed or right tailed b Find the P value c Using a significance level of a 0 10 should we reject Ho or should we fail to reject Ho Click here to view page 1 of the standard normal distribution table Click here to view page 2 of the standard normal distribution table a This is a test

In a clinical trial of a drug intended to help people stop smoking 132 subjects were treated with the drug for 12 weeks and 18 subjects experienced abdominal pain If someone claims that more than 8 of the drug s users experience abdominal pain that claim is supported with a hypothesis test conducted with a 0 05 significance level Using 0 15 as an alternative value of p the power of the test is 0 96 Interpret this value of the power of the test The power of 0 96 shows that there is a chance of rejecting the hypothesis of p when the true proportion is actually That is if the proportion of users who experience abdominal pain is actually then there is a chance of supporting the claim that the proportion of users who experience abdominal pain is than 0 08 Type integers or decimals Do not round

The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl In a clinical trial results could be analyze with a formal hypothesis test with the alternative hypothesis of p 0 5 which corresponds to the claim that the method increases the likelihood of having a girl so that the proportion of girls is greater than 0 5 If you have an interest in establishing the success of the method which of the following P values would you prefer 0 999 0 5 0 95 0 05 0 01 0 001 Why The P value of sample evidence that most strongly supports the hypothesis that the method effective is preferred because it corresponds to the

Assume a significance level of 0 1 and use the given information to complete parts a and b below Original claim The mean pulse rate in beats per minute of a certain group of adult males is 74 bpm The hypothesis test results in a P value of 0 0784 a State a conclusion about the null hypothesis Reject Ho or fail to reject Ho Choose the correct answer below O A Reject Ho because the P value is less than or equal to a OB Fail to reject Ho because the P value is greater than a OC Reject Ho because the P value is greater than OD Fail to reject Ho because the P value is less than or equal to

55 36 62 36 47 54 46 61 Evaluate Kara s claim using a hypothesis test Write the hypothesis for the test O Ho 55 Ha H 55 Ho H 55 Ha 55 O Ho H 55 Ha 55 O Ho H 51 591 H 51 591 OHO H 51 591 H 51 591 O Ho p 51 591 Ha U 51 591 What is the p value of this test round to 4 places Based on the sample data we should conclude that O There is sufficient evidence at the a 0 05 level that the average work week is less that 55 ho O There is not sufficient evidence at the a 0 05 level that the average work wook is in hours

llowing 0 5e F x 1 0 5e Part a 5 points Determine the PDF of X for x 0 Part b 5 points Find P X 2 x 0 X 0

bsite receives an average of 10 visits every minute The site manager starts to monitor the number of visits at 10 00 am Part a 2 5 points What is the probability of receiving 30 visits in the period between 10 00 and 10 05 am Part b 2 5 points What is the probability of receiving 15 visits in the period between 10 03 and 10 05 am if 10 visits were received in the period between 10 00 and 10 02 Part c 5 points What is the expected number of arrivals in the period between 10 00 and 10 08 am if 10 visits were received by 10 03 am How about variance

Two health insurance compete for the business of 1000 customers Assume that each customer chooses between the insurance providers independently and with indifference It is also assumed that each company is capable of providing high quality service for at most N customers Parta 5 points Using a binomial model find an expression for N that will guarantee that the probability of turning away a customer because of the limited capability of the company is less than 1 Part b 5 points Use the normal approximation to get a numerical value for N

nd 5 46 A homogeneous wire is bent into the shape shown Determine by direct integration the x coordinate of its centroid x a cos 0 y a sin 0 45 a 0 0 X y Fig P5 46 45 45 X

The accompanying data are x Cost cents per serving and y Fiber content grams per serving for 18 high fiber cereals rated by a magazine Fiber per Serving Cost per Serving 31 46 49 62 41 19 77 71 30 7 10 10 7 8 7 12 12 8 LAUSE SALT Cost per Serving 53 53 67 43 48 28 54 27 51 Fiber per Serving 13 10 8 12 7 14 7 8 8 a Construct a scatterplot of y Fiber grams per serving content versus x Cost cents per serving Based on the scatterplot how would you describe the relationship between fiber cost O The scatterplot suggests a strong negative linear relationship between fiber content and cost O The scatterplot suggests no relationship between fiber content and cost The scatterplot suggests a strong positive linear relationship between fiber content and cost

Ho 59 3 Ha 59 3 You believe the population is normally distributed but you do not know the standard deviation data 107 7 64 5 91 1 a What is the test statistic for this sample test statistic b What is the p value for this sample p value Round to 3 decimal places c The p value is Round to 4 decimal places O less than or equal to a O greater than a 0 05 d This test statistic leads to a decision to O reject the null O accept the null O fail to reject the null e As such the final conclusion is that O There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 59 3 There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 59 3 O The sample data support the claim that the population mean is greater than 59 3 O There is not sufficient sample evidence to support the claim that the population mean is greater than 59 3

3 A college wants to see if there is a significant difference in the amount of time an average full time student studies each week compared to the national average of 17 hours Given that a random sample of 140 students studied an average of 15 5 hours with a population standard deviation of 6 4 hours determine if there is a significant difference between this college and the national average Test at a 95 confidence level a 0 05 The null and alternative hypotheses Ho 17 a Compute the test statistic z score b What is the p value for the test statistic HA 17

equal to 70 points We claim they are incorrect to see if average improvement is different than 70 We randomly sample students for their average improvement The data we collected are below GRE scores are known to be normally distributed Points 60 9 72 4 74 54 3 57 2 61 2 70 8 65 4 63 1 67 4 73 7 Evaluate the company s claim using a hypothesis test You wish to test the following claim Ha at a significance level of a 0 05 a Write the hypothesis for the test OHO H 70 Ha 70 H 70 H 70 O Ho 70 Ha 70 HO H 65 491 Ha H 65 491 O Ho U 65 491 Ha 65 491 Ho 65 491 Ha 65 491

The Average Work Week Kara a newly hired engineer has been informed that the mean work week for engineers in start up companies is 55 hours Kara hopes that the mean hours worked per week is less than 55 hours She asks random engineers in start ups for the lengths of their mean work weeks The data are below Assume work time is normally distributed Hours 49 52 1444455 59 47 57 48 53 60 61 54 65 47 55 36 62 34545 36 47 46 61 Evaluate Kara s claim using a hypothesis test Write the hypothesis for the test O Ho H 55 Ha H 55 H 55 H 55 O Ho H 55 H u 55

Fresh Donuts A donut company says that their donuts remain fresh for over 2 days on average We tested a random sample of donuts for how long they remained fresh The data are below Assume donut freshness is normally distributed days 2 8 2 6 3 2 7 1 4 2 5 3 1 3 5 3 3 6 3 1 9 2 3 3 3 3 2 2 6 3 3 3 3 3 Evaluate the company s claim using a hypothesis test a Write the hypothesis for the test OH 2 Ha H 2 O Ho H 2 Ha H 2 Ho 2 Ha 2 O Ho U 2 847 Ha H 2 847 O Ho H 2 847 H 2 847

Fresh Donuts A donut company claims that their donuts remain fresh for more than 2 days on average A donut watchdog organization samples 12 donuts and finds that on average they remain fresh 2 8 days with a standard deviation of 1 1 days Evaluate the company s claim using a hypothesis test Use a 5 level of significance Assume that donut freshness follows a normal distribution a Write the hypotheses for the test OH H 2 Ha 2 O Ho H 2 8 H 2 8 O Ho 2 8 Ha 2 8 OH 2 Ha 2 O Ho 2 Ha 2 O Ho H 2 8 Ha H 2 8 b Compute the p value for the test P round to four decimal places c What is the final conclusion O There is sufficient evidence to support the company s claim O There is sufficient evidence to reject the company s claim There is not sufficient evidence to support the company s claim There is not sufficiel

Test Prep A GRE prep company advertises that average score improvement in GRE scores of their students is equal to 50 points A consumer group believes this is incorrect and randomly samples 40 students who have taken the GRE prep course from this company They find that the sample has an average improvement of 30 points with a standard deviation of 25 points Evaluate the consumer groups belief that the company s advertised score improvement is incorrect Use a 5 level of significance a Write the hypotheses for the test O Ho 50 H 50 O Ho 30 Ha 30 O Ho 50 Ha 50 O Ho H 30 Ha 30 Ho H 30 Ha 30 O Ho 50 Ha 50 b Compute the p value for the test p round to four decimal places c What is the final conclusion O There is not sufficient evidence to support the average score increase in GRE is not 50 points O There is not sufficient evidence to reject the average score increase in GRE is not 50 points There is sufficient evidence to support the average score increase in GRE is not 50 points

Nutrition labels The nutrition label on a bag of potato chips says that a serving of potato chips has 130 calories You believe this is incorrect and take a random sample of 53 bags that yielded a sample mean of 134 calories with a standard deviation of 17 calories Test the claim at a 5 level of significance that the number of calories listed on the nutrition label on a bag of potato chips is not correct a Write the hypotheses for the test Ho H 130 Ha 134 Ho 130 Ha H 134 O Ho o 17 Ha 0 17 Ho 130 Ha 130 b Compute the p value for the test p round to three sig figs c What is the final conclusion O There is not sufficient evidence to support the claim that the true average calorie content is different from 130 calories There is sufficient evidence to reject the claim that the true average calorie content is different from 130 calories There is not sufficient evidence to reject the claim that the true average calorie content is different from 130 calories O There is sufficient evidence to support the claim that the true average calorie content is different from 130 calories

You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly less than 0 52 You use a significance level of a 0 01 Ho p 0 52 H p 0 52 You obtain a sample of size n 193 in which there are 91 successes What is the test statistic for this sample Report answer accurate to three decimal places test statistic What is the p value for this sample Report answer accurate to four decimal places p value The p value is O less than or equal to a O greater than a This test statistic and p value lead to a decision to O reject the null accept the null O fail to reject the null As such the final conclusion is that O There is sufficient evidence to warrant rejection of the claim that the probability of a true negative on a test for a certain cancer is less than 0 52 There is not sufficient evidence to warrant rejection of the claim that the probability of a true negative on a test for a certain cancer is less than 0 52 The sample data support the claim that the probability of a true negative on a test for a certain cancer is less than 0 52

You wish to test the following claim Ha at a significance level of a 0 02 Ho 73 9 Ha 73 9 You believe the population is normally distributed but you do not know the standard deviation You obtain a sample of size n 14 with mean 66 7 and a standard deviation of s 11 3 a What is the test statistic for this sample test statistic b What is the p value for this sample p value Round to 3 decimal places c The p value is Use Technology Round to 4 decimal places O less than or equal to a Ogreater than a d This test statistic leads to a decision to O reject the null O accept the null fail to reject the null e As such the final conclusion is that O There is sufficient evidence to warrant rejection of the claim that the population mean is less than 73 9 O There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 73 9 O The sample data support the claim that the population mean is less than 73 9 O There is not sufficient sample evidence to support the claim that the population mean is less than 73 9

The Wechsler Adult Intelligence Scale IQ test is constructed so that Full Scale IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 15 The mayor of Smart Town believes the county s residents are smarter than the national average and wants to use it the intelligence of the residents as a marketing tool to bring industries to the area A researcher is hired to conduct a study to determine whether Smart County s residents have on average higher Full Scale IQs than the population A random sample of 100 people from Smart County were given the IQ test and were found to have an average Full Scale IQ of 105 a Which hypothesis test should be used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average F Oz test for the population mean Ot test for the population mean Oz test for the population proportion Ot test for the population proportion b What are the null and alternative hypotheses O Ho 105 Ha 105 Ho H 105 Ha 105 O Ho p 105 Ha 100 O Ho 100 Ha 100 c What is the value of the test statistic used to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average 0 333 O 333 03 33 O 3 33 d After analyzing the data to determine whether the mean Full Scale IQ score of the Smart County residents is higher than the national average the P value of 0004 was obtained Use a 0 05 O Do not reject the null hypothesis The average Full Scale IQ of Smart County residents is not higher than the population average O Do not reject the null hypothesis The average Full Scale IQ of Smart County residents is higher than the population average O Reject the null hypothesis The average Full Scale IQ of Smart County residents is not higher than the population average

2 10 pts We are told that 67 of the Missoula population has been skiing We are going to take a random sample of 120 students What does our random variable P represent in this instance a The random variable P represents the sample proportion of students who have gone skiing from the random sample of 120 students from the Missoula population b What does the distribution of P look like Justify your response Hint reference the CLT then draw the distribution with the mean and standard deviation clearly labeled Show work for us and op H 30 0 67 3 0 0429 0 5413 0 67 1 0 67 120 I 0 2211 120 0 0018125 0 0429 1 Hp 20p 0 67 2 0 0429 0 5842 I 1 0 67 1 0 33 1 0 67 0 0429 0 6271 120 I H 0 67 1 Hp p 0 67 0 0429 0 7129 I 1 Hp 20p 0 67 2 0 0429 0 7558 I 0 5413 0 5842 0 6271 0 67 0 7129 Hp 30 0 67 3 0 0429 0 7987 1 mean 0 7558 1 I c What s the probability that 89 or fewer in our sample have gone skiing before Hint what is our sample statistic p Label shade in the corresponding area on your distribution above then show your work calculation below 0

Making handcrafted pottery generally takes two major steps wheel throwing and firing That is the time for a piece of pottery to be finished is the sum of the time associated with these two steps The time for wheel throwing and the time for firing are each normally distributed random variables with means of 50 min and 70 min and standard deviations of 5 min and 7 min respectively That is if we let the random variable X represent the time for wheel throwing then X N 50 25 Furthermore if we let the random variable Y represent the time for firing then Y N 70 49 Part a 5 points Assuming the time required for wheel throwing and firing are independent what is the probability that a piece of pottery will be finished within 110 minutes Part b 5 points Let X denote the wheel throwing time required for the i th piece of pottery produced Suppose X N 50 25 for each i and the X variables are independent of each other Let X denote the average wheel throwing time required by the first 5 pieces of pottery What is P 53

38 The probability that an individual randomly selected from a particular population has a certain disease is 05 A diagnostic test correctly detects the presence of the disease 98 of the time and correctly detects the absence of the disease 99 of the time If the test is applied twice the two test results are independent and both are positive what is the posterior probability that the selected individual has the disease Hint Tree diagram with first generation branches corresponding to Disease and No Disease and second and third generation branches corresponding to results of the two tests

Suppose we have a random sample of size 2n from a population denoted by X and E X and V X 0 Let X X 2n 2n 2 i 1 n X X i 1 be two estimators of u Which is the better estimator of Explain your choice in terms of bias and variance

Many investors and financial analysts believe the Dow Jones Industrial Average DJIA gives a good barometer of the overall stock market On January 31 2006 9 of the 30 stocks making up the DJIA increased in price The Wall Street Journal February 1 2006 On the basis of this fact a financial analyst states we can therefore assume that 30 of the stocks traded on the New York Stock Exchange NYSE went up the same day A sample of 54 stocks traded on the NYSE that day showed that 12 went up You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0 3 You use a significance level of a 0 01 What is the test statistic for this sample Report answer accurate to three decimal places test statistic What is the p value for this sample Report answer accurate to four decimal places p value The p value is O less than or equal to a greater than a This test statistic and p value lead to a decision to Oreject the null O accept the null O fail to reject the null As such the final conclusion is that O There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is less than 0 3 There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is less than 0 3 O The sample data support the claim that the proportion of stocks that went up is is less than 0 3

0 9 Is It Significant The one sample t statistic from a sample of n 3 observa tions for the two sided test of Ho 50 Ha 50 has the value t 2 10 a What are the degrees of freedom for t b Locate the two critical values t from Table C that bracket t What are the two sided P values for these two entries c Is the value t 2 10 statistically significant at the 10 level At the 5 level At the 1 level d Optional If you have access to suitable technology give the exact two sided P value for t 2 10

1 Travel Time to Work A study of commuting times reports the travel times to work of a random sample of 1000 employed adults in Seattle The mean is x 37 9 minutes and the standard deviation is s 27 2 minutes What is the standard error of the mean

29 Wearable technology and weight loss Do wearable devices that monitor diet and physical activity help peo ple lose weight Researchers had 237 subjects already involved in a program of diet and exercise use wear able technology for 24 months They measured their weight in kilograms before using the technology and 24 months after using the technology 18 a Explain why the proper procedure to compare the mean weight before using the wearable technology and 24 months after using the wearable technology is a matched pairs t test b The 237 differences in weight weight after 24 months minus weight before using the wearable technology had x 3 5 and s 7 8 Is there significant aidanan ol

20 49 Right versus 4step ments affects how easily people can use them Timothy Sturm investigated this effect in a course project asking 25 right handed students to turn a knob with their right hands that moved an indicator by screw action There were two identical instruments one with a right hand thread the knob turns clockwise and the other with a left hand thread the knob turns counterclockwise Table 20 4 gives the times in sec onds each subject took to move the indicator a fixed distance RTLFT TABLE 20 4 Performance times seconds using right hand and left hand threads Right Subject Thread 1 113 2 105 3 130 4 101 5 138 6 118 7 87 8 116 9 75 10 96 11 122 12 103 13 116 Left Thread 137 105 133 108 115 170 103 145 78 107 84 148 147 Subject 14 15 16 17 18 19 20 21 22 23 24 25 Right Left Thread 107 118 103 111 104 111 89 78 100 89 85 88 Thread 87 166 146 123 135 112 93 76 116 78 101 123

The manager of a 100 unit apartment complex knows from experience that all units will be occupied if the rent is 900 per month A market survey suggests that on average one additional unit will remain vacant for each 10 increase in rent What rent in dollars per month should the manager charge to maximize revenue per month

The average number of calories from a fast food meal for adults in the US is 840 calories A nutritionist believes that the average is higher than reported They randomly sampled 49 meals that adults ordered and found the data below Use a 1 significance level to test this belief Click here to open the data in StatCrunch 849 857 852 859 838 874 853 847 857 812 849 919 873 815 903 827 849 849 839 804 905 802 822 811 856 766 846 913 867 887 822 844 803 875 879 937 850 837 841 913 838 849 864 844 904 793 866 826 909 t stat round to 2 decimal places 2 53 A p value do not round 0 007 A

A candidate for political office wants to determine if there is a difference in her popularity proportion between millennials and baby boomers To test the claim of this difference she conducts a survey of voters The sample contains 515 millennials and 650 baby boomers of which 285 of the millennials and 340 of the baby boomers favor her candidacy Do these values indicate a significant difference in popularity between these two groups Use a 0 05 significance level z stat round to 2 decimal places 2 0339 p value do not round 0 0424 A reject ho A What is your decision Retain Ho or Reject Ho A Question 10 0 75 points Give a summary statement for the hypothesis test in the prior problem Be sure to use the context of the problem

Suppose the coffee industry claimed that the average adult drinks 2 5 cups of coffee per day Because of other choices of caffeine beverages marketers believe that college students drink less cups of coffee per day A random sample of 100 college students was selected and the sample mean was 2 4 cups per day with a standard deviation of 0 75 cups per day Use a 0 05 significance level to test the marketers belief t stat round to 2 decimal places 1 33 p value do not round 0 0927 A retain ho A What is your decision Retain Ho or Reject Ho N Question 7 0 75 points Write a summary statement for this bu

Cereal for Breakfast A cereal company announced 60 of Americans start the day with cereal for breakfast You believe the percentage of Americans that start the day with cereal is less To test your claim you randomly sample 100 Americans and ask them what they eat for breakfast 45 of them say cereal Test your claim that percent of Americans that start the day with cereal for breakfast is less than 60 at a 5 level of significance a Select the correct null and alternative hypotheses O Ho P 0 45 Ha p 0 45 O Ho P 0 6 H P 0 6 Ho P 0 45 Ha p 0 45 Ho p 0 6 Ha p 0 6 Ho p 0 45 Ha p 0 45 O Ho P 0 6 Ha p 0 6 b Find the p value round to four decimal places c Write the final conclusion using everyday language O There is sufficient evidence to reject your claim There is not sufficient evidence to support your claim There is not sufficient evidence to reject your claim There is sufficient evidence to support your claim