UW-Madison STAT 324 - hw1 (5 pages)

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Pages:
5
School:
University of Wisconsin, Madison
Course:
Stat 324 - Intro Applied Stat for Engineers
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Homework 1 Due Wednesday June 27th at 4 pm Submit your homework on Canvas or to your TA s mailbox before to the due date time The mailboxes are to the left as you enter the Medical Science Center 1300 University Ave from the main University Ave entrance No late homework will be accepted for credit If a problem asks you to use R include a copy of the code and output Please edit your code and output to be only the relevant portions If a problem does not specify how to compute the answer you may use any appropriate method I may ask you to use R or manual calculations on exam so practice accordingly 1 If you wanted to estimate the mean height of all the students at a university which one of the following sampling strategies would be best Why Note that none of the methods are true simple random samples a Measure the heights of 50 students found in the gym during basketball intramurals b Measure the heights of the engineering majors c Measure the heights of the students selected by choosing the first name on each page of a campus phone book 2 A zoologist collected wild lizards in the Southwestern United States Thirty lizards from the genus Phrynosoma were placed on a treatmill and their speed measured The recorded speeds meters second the fastest time to run a half meter for the thirty lizards are summarized in the relative histogram below Courtesy of K Bonine 1 a Is the percent of lizards with recorded speed below 1 25 closest to 25 50 or 75 b In which interval are there more speeds recorded 1 5 1 75 or 2 2 5 c About how many lizards had recorded speeds above 1 meters second 3 In a sample of 20 men the mean height was 178 cm with standard deviation of 6 cm In a sample of 30 women the mean height was 164 cm with standard deviation of 6 cm If both samples were combined into one larger group a What is the mean height for the combined group b The standard deviation for the combined group would be hint do not do any calculations just try to sketch rough histograms for each sample separately and then one for the combined sample i ii iii iv Less than 6 cm Greater than 6 cm Equal to 6 cm Can not tell from the information given 4 After manufacture computer disks are tested for errors The table below gives the number of errors detected on a random sample of 100 disks Number of Defects Frequency 0 41 1 31 2 15 3 8 4 5 a What is the shape of the histogram for the number of defects observed in this sample b Calculate the mean and median number of errors detected on the 100 disks How do these values compare and is that consistent with what we would guess based on the shape c Calculate the sample standard deviation with your calculator and R Are the values consistent between the two methods Explain what this value means in the context of the problem d Calculate the first and third quartiles and IQR by hand and with R Are the values consistent betweeen the two methods Explain what the three values mean in the context of the problem e What proportion of the computer disks had a number of errors greater than the mean number of errors 2 f What range of values for this sample data are not considered outliers using the Q1 1 5IQR Q3 1 5IQR designation using the IQR you calculated by hand g Sketch a boxplot of the data by hand using the relevant values you calculated by hand 5 Physical education researchers interested in the develoment of the overarm throw measured the horizontal velocity of a thrown ball at the time of release The results for first grade children in feet sec courtesy of L Halverson and M Roberton are Males 54 2 39 6 52 3 48 4 35 9 30 4 25 2 45 4 48 9 48 9 45 8 44 0 52 5 48 3 59 9 51 7 38 6 39 1 49 9 38 3 Females 30 3 43 0 25 7 26 7 27 3 31 9 53 7 32 9 19 4 23 7 23 3 23 3 37 8 39 5 33 5 30 4 28 5 a Use R to create a histogram for the males and a histogram for the females any kind of histogram that you want Adjust the x axis scale so the two groups are more easily compared b Compare the shape of the throws from the male and female students observed in this sample c Compute and compare the mean and median throw velocities observed in the male and famale students across gender d Compute and compare the standard deviation in throw velocities observed in the male and famale students e Use R to help you create a boxplots of the two sets so they are easily comparable f Which if any values were identified as outliers Would this value have been identified as an outlier if it were thrown by the opposite gender g What would be the shape of the histogram had we combined the boys and girls throw velocities into one large data set with 37 values 6 A geologist weighs a specimen sample five times The readings in grams are 48 5 47 2 4 91 49 5 and 46 3 Which measures of center and spread will be highly affected by this outlier and thus give a clue that they have an entry error 7 A campus organization will select one day of the week for an end of year picnic Assume that the weekdays Monday through Friday are equally likely and that each weekend day Saturday and Sunday is twice as likely as a weekday to be selected 3 a Assign probabilities to the seven outcomes b Find the probability a weekday will be selected 8 Comparing observed data to a theoretical model a Consider the simplistic model that human births are evenly distributed over the 12 calendar months each person has an equal chance of being born in each month If a person is randomly selected say from the phone directory what is the probability that his or her birthday would be i In a winter month start of November end of February ii Not over the summer where summer is start of May end of August b The following record shows a classification of births in thousands in the United States Calculate the relative frequency of births for each month and comment on the plausibility of a uniform probability model each month has the same probability Jan Feb March April May June July Aug Sept Oct Nov Dec Total 331 5 309 6 349 3 332 5 346 3 350 9 357 1 369 3 363 4 344 6 335 7 348 3 4 138 5 9 The following frequency table shows the classification of 58 landfills in a state according to their concentration of the …


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