Stats_HW1

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Apr 3, 2024

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PSYC 2320 Sta+s+cs in Psychological Research Homework #1 (Upload a pdf to the Homework #1 assignment) 1. What are descrip+ve sta+s+cs? What are they used for? Descrip+ve sta+s+cs are a set of tools that are used to summarize and describe the characteris+cs of a set of data. They are used to provide a quick overview of the main features of a dataset, and include measures such as the mean, median, mode, and standard devia+on. 2. What are inferen+al sta+s+cs? What are they used for? Inferen+al sta+s+cs are a set of tools that are used to make inferences and draw conclusions about a general popula+on based on a sample of data. They are used to make generaliza+ons about the general popula+on to test hypotheses and make predic+ons. 3. Suppose I wanted to know how much +me my sta+s+cs students spend on homework this term. I ask my sta+s+cs class of 40 students how many hours they spent on homework last week. Is my sta+s+cs class a sample or a popula+on? Why? Your sta+s+cs class is a sample of the popula+on of all the sta+s+cs students in the term. That is because you have chosen just one class (subset) of students to gather informa+on about the +me they spend on homework. 4. For each of the following, indicate whether a set of such observa+ons would yield qualita+ve or quan+ta+ve data: a. Poli+cal affilia+on: Qualita+ve b. Reac+on +me: Quan+ta+ve c. Sizes of pizzas (sm, lg) ordered at UHOP last week: Qualita+ve d. Hours spent watching TV: Quan+ta+ve 5. For each of the following variables, indicate the level of measurement (nominal, ordinal, interval/ra+o):
a. Number of points scored per game by NU Women’s Hockey team last season. Interval b. Movie ra+ngs (like R or PG-13) Ordinal c. Sta+s+cs students’ favorite colors Nominal d. Birth weights Ra+o 6. Which of the following variables are discrete and which are con+nuous? a. Time spent brushing your teeth Con+nuous b. Number of dogs on campus Discrete c. Fuel consump+on (miles per gallon) Con+nuous 7. A researcher is interested in finding out what the effect of phone use in class is on performance. They randomly assign students to groups that either: 1. Were asked to store their phone in their backpack, 2. Were asked to silence no+fica+ons and keep the phone on the desk, or 3. Were asked to keep their phone on the desk with no+fica+ons on. Everyone watched a videotaped lecture on bird migra+on. Afer the lecture the researcher recorded the number of correct answers each student gave on a quiz about bird migra+on. a. In this experiment, what is the independent variable? The phone, whether it is in the backpack, silenced, or no+fica+ons on b. What is the dependent variable? Number of correct answers on the quiz c. What type of data do they have (qualita+ve or quan+ta+ve)? Quan+ta+ve, quiz scores
d. At what level of measurement? Ra+o 8. Suppose I gathered data on the number of hours a month faculty in the Psychology Department spent playing Wordle. Using the table below, create a grouped frequency distribu+on using these data. Include frequency, rela+ve frequency (expressed in percent) and cumula+ve rela+ve frequency (expressed in percent). Use about 6 classes with a width of 5. The lower boundary for the first class is provided in the table . a. I suggested 6 classes, a class width of 5 and to begin the lowest class in the table with a boundary of 5. How did I arrive at those numbers? Because the range is 27, so you divided 27/6 = 4.5 because you wanted 6 classes to represent the data and then you rounded up to 5. b. Fill in the following table: 34 22 19 15 13 12 32 22 18 15 13 12 30 22 18 15 13 12 30 22 18 15 13 12 24 20 17 14 12 10 24 20 17 14 12 9 24 20 16 14 12 8 23 19 16 14 12 7 Hours spent on Wordle Frequency ( f ) Rela+ve f (%) Cumula+ve rela+ve f (%) 35 - 39 0 0 0 30 - 34 4 8.33 8.33 25 - 29 0 0 8.33 20 - 24 11 22.92 31.25
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c. Which class contains the score at the 50 th percen+le? 9. For the following exam scores, compute the mode, median and mean. Which measure of central tendency should be used with cau+on when describing this set of scores? Why? 79, 91, 89, 82, 76, 96, 83, 42, 89, 95 Mode: 89 Median: 89 Mean: 84.5 The mean should be used with cau+on when describing this set of scores because there is an outlier, 42, that significantly affects the mean. The mode and median are not affected by outliers. 10. For the following data set: 10, 7, 3, 5, 9, 2, 25 a. Show that Σ (x - x̅) = x̅ = (10 + 7 + 3 + 5 + 9 + 2 + 25) / 7 = 10 To find Σ (x - x̅), we will subtract x̅ from each value in the data set and sum the results. (10 - 10) + (7 - 10) + (3 - 10) + (5 - 10) + (9 - 10) + (2 - 10) + (25 - 10) = 0 + (-3) + (-7) + (-5) + (-1) + (-8) + 15 = -10 So Σ (x - x̅) = -10 11. For each of the three distribu+ons listed below, use the measures of central tendency to determine whether or not there is evidence of skew and, if there is skew, what direc+on (posi+ve or nega+ve) it is. 15 - 19 13 27.08 58.33 10 - 14 17 35.42 93.75 5 - 9 3 6.25 100 Total f = 48
Distribu+on A: Mean = 54 Median = 62 Nega+ve skew because mean < median Distribu+on B: Mean = 68 Median = 60 Posi+ve skew because mean > median 12. Consider the data set below to be a sample. 2, 10, 8, 2, 3, 4, 5, 7 a. Calculate the range. 10 - 2 = 8 b. Calculate the standard devia+on using the defini+onal formula for the sum of squares. Include the calculated sum of squares . First we find the mean, (2 + 10 + 8 + 2 + 3 + 4 + 5 + 7) / 8 = 5.125 Then sum of squares: (2 - 5.125)^2 + (10 - 5.125)^2 + (8 - 5.125)^2 + (2 - 5.125)^2 + (3 - 5.125)^2 + (4 - 5.125)^2 + (5 - 5.125)^2 + (7 - 5.125)^2 = 60.875 Then standard devia+on: √(60.875/8-1) = √(60.875/7) = √8.696 = 2.95 13. Given the following grouped frequency distribu+on, I made a histogram (below). Can you find the 4 things I did wrong on the histogram? ages in months frequency 22 to 23 2 20 to 21 0 18 to 19 6 16 to 17 10
1. Numerical scales are increasing from right to lef instead of from lef to right 2. Adjacent bars do not share boundaries 3. Did not label x and y axis 4. Frequency intervals on the y axis are not consistent Last one! Open up the Excel spreadsheet “Excel homework #1 You will find the Wordle data from Ques+on 8 and a table for you to enter your grouped frequency distribu+on. Treat the data as a sample. When you’re done, please upload your excel file to the Homework #1 assignment, 14 to 15 8 12 to 13 1 Total 27 0 3 5 8 10 22 to 23 18 to 19 16 to 17 14 to 15 12 to 13
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1. Use formulas to calculate the sum (∑x), mean, median, mode, standard devia+on, and variance in cells next to the data. 2. Use the grouped frequency distribu+on from Ques+on 7 to create a histogram (remember: you will have to reorder the groups in order to make your X-axis correctly)