Name: E number: Math 1530 section number MATH 1530 CAPSTONE TECHNOLOGY PROJEC T SUMMER 2015 Problem 1 : Identify Variable Type. One of these is a variable that is categorical and one is quantitative. Consider the different graphs that correspond to each variable type. Use Minitab to create two different graphs appropriate for each variable’s type. EXTRA CRED IT if you can resize to fit all of the graphs on one page. NUCLEAR SAFETY TALK POLITICS Nuclear Safety is a categorical variable. And the talk politics is a quantitative variable, the appropriate graphs are given below. Problem 2 : Sampling. In the survey data, the variable “AGE” is the current age reported by each student. a. Type the first 10 observations from the column representing the variable AGE into the table below, and use this as your sample data for part (b) . Then calculate the mean age of these first 10 observations and report the value below. N 1 2 3 4 5 6 7 8 9 10 AGE (yrs) 20 18 19 19 26 19 20 20 19 19 E x t r e m e l y s a f e M o d e r a t e l y s a f e N o t a t a l l s a f e S l i g h t l y s a f e V e r y s a f e C a t e g o r y P i e C h a r t o f N U C L E A R S A F E T Y V e r y s a f e S l i g h t l y s a f e N o t a t a l l s a f e M o d e r a t e l y s a f e E x t r e m e l y s a f e 3 0 0 2 5 0 2 0 0 1 5 0 1 0 0 5 0 0 N U C L E A R S A F E T Y C o u n t C h a r t o f N U C L E A R S A F E T Y 7 6 5 4 3 2 1 0 3 0 0 2 5 0 2 0 0 1 5 0 1 0 0 5 0 0 T A L K P O L I T I C S ( d a y s ) F r e q u e n c y H i s t o g r a m o f T A L K P O L I T I C S ( d a y s ) 7 6 5 4 3 2 1 0 T A L K P O L I T I C S ( d a y s ) B o x p l o t o f T A L K P O L I T I C S ( d a y s ) Name: E number: Math 1530 section number b. The mean age of the first 10 students is 19.9 years. (Type the value into the space provided.) c. Identify the type of sampling method you have just used: This is an example of convenience sampling. d. Next, select a random sample of size n = 10 (Go to Calc > Random Data > Sample from Columns). Type the number 10 in the “Number of rows to Sample” slot. Enter the variable “ID” and “AGE” into the “From columns” slot. Enter C17 - C18 into the “Store samples in” slot. Record the data for your sample in the table below. N 1 2 3 4 5 6 7 8 9 10 ID 662 48 206 636 49 209 422 414 279 565 AGE (yrs) 24 18 18 35 19 48 18 18 18 19 e. Calculate and report the mean age for your random sample of 10 students. The sample mean age is 23.5 years. f. Identify the type of sampling method you have just used: This is an example of simple random sampling. g. REPEAT the random sample selection process three more times. Calculate and report the mean age for each random sample of 10 students. N 1 2 3 4 5 6 7 8 9 10 ID 590 63 242 723 299 43 337 711 549 741 AGE (yrs) 19 19 35 20 20 25 20 24 18 20 ii) The sample mean age is 22 years. N 1 2 3 4 5 6 7 8 9 10 ID 344 169 754 697 686 564 6 372 493 570 AGE (yrs) 19 22 18 18 19 19 19 22 58 22 iii) The sample mean age is 23.6 years. N 1 2 3 4 5 6 7 8 9 10 Name: E number: Math 1530 section number ID 627 292 209 212 406 281 40 419 704 331 AGE (yrs) 19 21 48 20 19 21 18 21 18 19 iv) The sample mean age is 22.4 years. h. Suppose we think of all the students who responded to the survey as a population for the purposes of this problem. In that case, the population mean age i s 21.293. Discuss (two or more complete sentences) the difference s and similarities between 21.293 and the answers you got in (b), (e), and ii), iii), and iv). The samples we have collected in (b), (e), and ii), iii), and iv) are just a part of the complete population data. Thus the obtained samples means may or may not be exactly equal to the population mean, here we can see that the sample means are very close to the population mean but not exactly equal. The samples means thus can be considered as an estimate of the population mean. Problem 3(h) : FL IP A COIN. Circle the outcome heads / tails. If you got ‘heads,’ then do this problem. (Omit t his page/problem if you got ‘tails . ’ ) Question 10 of the SPRING 2015 survey asked students, “ How much money did you spend on your last clothing purchase? (in US dollars) ” a. Create an appropriate graph to display the distribution of the variable called CLOTHING PURCASE and insert it here. The obtained graph is given below, b . Which of the following best describes the shape of the distribution? Underline your answer. Skewed left Symmetric Skewed right c . Using Minitab, calculate the basic statistics for the data collected on CLOTHING PURCASE . Copy and paste all of the Minitab output here. $ 1 , 8 0 0 . 0 0 $ 1 , 5 0 0 . 0 0 $ 1 , 2 0 0 . 0 0 $ 9 0 0 . 0 0 $ 6 0 0 . 0 0 $ 3 0 0 . 0 0 $ 0 . 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 0 C L O T H I N G P U R C H A S E F r e q u e n c y H i s t o g r a m o f C L O T H I N G P U R C H A S E Name: E number: Math 1530 section number Descriptive Statistics: CLOTHING PURCHASE Variable N N* Mean SE Mean StDev Variance CoefVar Minimum Q1 Median CLOTHING PURCHASE 795 5 65.39 3.84 108.20 11707.90 165.48 0.00 20.00 36.00 N for Variable Q3 Maximum Range IQR Mode Mode Skewness Kurtosis CLOTHING PURCHASE 75.00 2000.00 2000.00 55.00 20 96 9.05 136.14 d . Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of CLOTHING PURCASE . Which statistic will you use to describe the center of the distribution? ( Median ) e . What is the value of that statistic? ( 36 ) f . Which statistic(s) will you use to describe the spread of the distribution? Range or IQR. g . What is (are) the value(s) of that (those) statistic(s)? Range = 2000 and IQR = 55 h . Look up the IQR rule on p. 50 in our textbook. Are there any outliers in this distribution? If so, what are their values? How many are there? Justify your answer. Using IQR rules, Acceptable lower limit = Q1 - 1.5*IQR = 20 - 1.5*55 = - 62.50 As all values are above this limit so there are no outliers on the lower side. Acceptable upper limit = Q3+1.5*IQR = 75+1.5*55 = 157.5 There are 70 values above this acceptable limit and all of them are outliers. Problem 3(t ) : YOU JUST FLIP PED A COIN . If you got ‘tails,’ then do this problem. (Omit t his page/problem if you got ‘heads . ’ ) Question 12 of the FALL 201 4 survey asked students, “ Usually, how many hours sleep do you get in a night? ” The data is in column 1 4 ‘SLEEP’ o f the data file. Name: E number: Math 1530 section number a. Create an appropriate graph to display the distribution of the variable called SLEEP and insert it here. The obtained graph is given below, b . Which of the following best describes the shape of the distribution? Underline your answer. Skewed left Symmetric Skewed right c . Using Minitab, calculate the basic statistics for the data collected on SLEEP and copy & paste the Minitab output here. The obtained output is given below, Descriptive Statistics: SLEEP Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum SLEEP 1184 0 6.5853 0.0387 1.3328 2.0000 6.0000 7.0000 8.0000 14.0000 d . Choose statistics that are appropriate for the shape of the distribution to describe the center and spread of SLEEP . i) Which statistic will you use to describe the center of the distribution? ( Mean ) ii) What is the value of that statistic? ( 6.5853 ) iii) Which statistic(s) will you use to describe the spread of the distribution? Standard deviation 1 4 1 2 1 0 8 6 4 2 3 5 0 3 0 0 2 5 0 2 0 0 1 5 0 1 0 0 5 0 0 S L E E P F r e q u e n c y H i s t o g r a m o f S L E E P