MA 2113 Homework #1
Table 1. List of NFL divisions that have won the Superbowl over the past 52 years.
NFC North AFC West NFC East NFC North AFC South NFC North NFC East NFC East AFC West NFC East AFC East AFC North NFC West AFC West AFC North AFC West AFC North NFC West AFC West NFC South AFC South AFC West NFC East AFC North NFC North NFC East NFC West NFC East AFC East NFC East AFC East NFC East NFC East NFC South AFC North AFC East AFC West NFC East AFC East NFC West AFC North NFC West NFC West AFC East AFC East AFC North NFC North NFC East AFC North AFC West AFC East NFC East
1. What type of data is this? Quantitative or Qualitative
2. Calculate the relative frequency and percentage by class.
3. Construct a bar graph of the relative frequencies by class.
Relative Class Frequency % Frequency
Table 2. Test scores from Exam 2 from a Wildlife Science class.
74 88 41 78 87 59 68 58 73 71 64 70 87 68 86 79 79 64 50 85 85 46 79 85 58 96 62 57 83 82 72 49 64
4. What type of data is this? Quantitative or Qualitative
5. Calculate relative frequency of scores by class. You determine the class intervals, so you do not have to use all rows or you can add some.
6. Construct a histogram of relative frequency of scores by class.
MA 2113 Homework #2 Be sure to show all tables and calculations! Table 1. Average annual OPEC crude oil price from 1990 to 2018 (in U.S. dollars per barrel). Year Price 1990 22 1991 19 1992 18 1993 16 1994 15 1995 17 1996 20 1997 19 1998 12 1999 17 2000 28 2001 23 2002 24 2003 28 2004 36 2005 51 2006 61 2007 69 2008 94 2009 61 2010 77 2011 107 2012 109 2013 106 2014 96 2015 50 2016 41 2017 53 2018 71
1. What is the mean and standard deviation for average annual price?
2. What is the median and Five-number Summary (quartiles) for annual price? MA 2113 Homework #3
1. Determine outliers, if any, and construct a boxplot for the following data.
Table 1. Number of fish found in 16 small streams on Tombigbee National Forest in 2003 while sampling the fish community with a seine net.
547 603 15 357
385 130 160 183 281 365 1113 1100 140 320 161 78
2. For the following equations provide: a) y-intercept and slope (don’t forget to do this!) b) a graph of the equation (plot at least 2 points other than the y-intercept) y = 2 + 2x y = 6 – 4x y = 1.5x – 3 y = x – 4
ST 2113 Homework #4 1. Calculate a regression equation using the (x, y) data below (8 points). We are interested to see if age of a used vehicle (x) has any relationship to cost (y). To check if you have done your work correctly, this should be your answer: ŷ = 220.9 – 14.6 x
Of course, show all your work.
Table 1. I went to AutoTrader.com and searched for used car prices for my type of vehicle, a Nissan XTerra. I searched for used XTerra’s from 2 (2014) – 10 (2006) years of age within 100 miles of Meridian. I recorded the first ten ages (x) and prices (y) the search produced. For easier calculations, prices are given in $100’s.
2. Graph a scatterplot of the data along with the regression line from the regression equation (2 points).
MA 2113 Homework #5
1. Compute the coefficient of determination (r2) for the regression equation calculated using the data below.
Table 1. Size, x, in hundreds of square feet and price, y, in thousands of dollars from a random sample of 9 custom homes listed for sale in Phoenix, AZ.
Size (x ) Price (y ) 26 520 27 605 33 555 29 627 29 586 34 711 30 718 40 854
22 476
Hint: You will need to first calculate the regression equation as you did in Homework #4 (using the table 2 above). You should get b1 = 19.1 and b0 =55.0. For the regression coefficient below, you should get r = 0.7266 or 72.7%.
Price (y ) 520 605 555 627 586 711 718 854
476
MA 2113 Homework #6
1. Compute the Pearson correlation coefficient, r, for the data below.
Table 1. Data from homework #5, size, x, in hundreds of square feet and price, y, in thousands of dollars from a random sample of 9 custom homes listed for sale in Phoenix, AZ. x y 26 520 27 605 33 555 29 627 29 586 34 711 30 718 40 854
22 476 To check your final answer, r = 0.8538 X 100 = 85.4%
ST 2113 Homework #7 Name:______
Mississippi has 235 high schools that report mean ACT scores for graduating seniors. I have grouped the schools by their mean ACT score rounded to the nearest whole number (e.g., in the first row, there are 13 high schools with a mean ACT score of 15). (Hint: μ = 18.74)
Reminder: You will have a quiz over this procedure when we meet for class after Spring Break on March 18. Please, contact me if you need help or would like me to send your graded homework via e-mail to study before the quiz.
What is the population mean (μ) and SD (σ) for this population?
ACT Freq Score x (Count) 15 13
16 36 17 26 18 29
19 29
20 50 21 31
22 16
23 4 24 1
MA 2113 Homework #8 Name:______1. Find the area under the standard normal curve for the following: a) Between z = 0 and z = 1.2 b) Between z = -0.48 and z = 1.2 c) ≥ z = 1.79 d) ≥ z = -1.65 e) ≤ z = 0.2 f) ≤ z = -0.4
2. Find the nearest z-score for the following areas under the standard normal curve: a) 0.1000 b) 0.9000
3. The mean length for imprisonment for motor-vehicle theft offenders in the U.S. is 16.7 (μ) months with a population SD of 6.0 months (σ). Prison term lengths are normally distributed. a) What is the z-score that corresponds to 12 months?______24 months?______
b) What is the area under the normal curve that corresponds to each of these z-scores? 12 months______24 months______
c) What is the % of offenders that spend between 8 to 12 months in prison for motor theft?
d) What % of offenders spend >18 months in prison?
e) What % of offenders spend <6 months in prison?
f) What is the cut-off time in number of months (x) for the bottom 25% of prison terms served for motor theft?
MA 2113 Homework #9 Name:______From the data set of Exam 1 test scores from 266 students in an Intro Statistics course, I randomly drew 30 values (on second page). From the entire population of scores where μ = 91.7 and σ = 20.0. a) Determine sample mean ( x ) and SD (s) using the 30 random values. You will not use s on this homework but you will on Homework #10.
b) Calculate a 90% CI using population SD, σ.
c) Calculate a 99% CI using population SD, σ.
d) Does μ fall into your CI?
x 105 94 110 96 104 34 107 92 110 107 88 85 109 104 89 89 60 84 106 88 84 108 104 106 91 99 51 108 95 106
MA 2113 Homework #10 Name:______
1. Construct confidence intervals (CI) from the sample data set from Homework # 9 (Exam 1 test scores from 30 of 266 students) with x = 93.8 and s = 17.7. From the entire population of scores, μ = 91.7 and σ = 20.0.
a) Calculate a 95% CI using sample SD, s.
b) Calculate a 99% CI using sample SD, s.
c) Does μ fall into your CI?
MA 2113 Homework #11 Name:______
A psychology study suggests that people who move from home to home frequently as children tend to have lower than average levels of well-being as adults. The study looked at a sample of 24 young adults who each experienced 5 or more different homes before age 16. The participants were given a standardized well-being questionnaire for which the general population has an average score of μ = 42.4 and σ = 2.3. We averaged the scores from the sample population for a sample mean ( x ) = 37.0. We will assume the standard deviation for this population is the same as the general population standard deviation (σ).
Using a significance level of 5% (α = 0.05, 95% confidence level), are we very confident that the sample mean from people who moved from home to home is statistically the same as the general population mean? Use the formula for z-test with known σ to make the decision.
MA 2113 Homework #12 Name:______
Using the same sample data from Homework #11, (24 participants with = 37.0), test the hypothesis that the mean scores for well-being for people who moved from home to home is statistically the same as the general population mean using a t-test. The sample standard deviation was s = 3.14. For the general population μ = 42.4 and σ = 2.3.
Using a significance level of 10% (α = 0.10, 90% confidence level), are we very confident that the sample mean from people who moved from home to home is statistically the same as the general population mean?