Math 001B Assignment 5.2 Name_________________________ DIRECTIONS To receive full credit, you must provide complete legible solutions to the following problems in the space provided. Transfer all your answers to the space provided on the test paper. 1. Express the limit as a definite integral on the given interval. Ans____________________ 2. Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your sample points.) Ans____________________ 3. Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the Midpoint endpoints of each subinterval as your sample points.) Ans____________________ 4. Evaluate the integral by interpreting it in terms of areas. a. Ans____________________ b. Ans____________________ 5. Use the limit of a Riemann sum and a left end point evaluation to find the value of the integral. Ans____________________ PSYCH 3610 - Statistics For Behavioral Sciences Dr. Peter Young Simpson University TAKE-HOME EXAM: Section 4 For each problem, show all of your work; use separate paper and circle all answers. 1. There have been a number of studies on the adjustment problems (that is, \"jet lag\") people experience when traveling across time zones. Jetlag always seems to be worse when traveling east. Consider this hypothetical study. A researcher examines how many days it takes a person to adjust after taking a long flight. Each subject is exposed to three flights over a period of 6 months: one that takes them east across time zones (California to New York), one that takes them west across time zones (New York to California), and one that takes a long flight within time zones (San Diego to Seattle). The following data represent the number of days it took for a person to adjust. Subject A B C D E F Westbound 2 1 3 3 2 4 Type of Flight Eastbound 6 4 6 8 5 7 Same Time Zone 1 0 1 1 0 0 Conduct a One-Way Repeated Measures ANOVA at the .01 level; cover all elements on Handout. 2. A researcher wanted to study the impact of different tempos of music at work on worker's sense of job satisfaction. Workers were told that they were going to be asked about their job satisfaction throughout the year, but were unaware that music tempos were going to be varied. Throughout the year, workers were asked to rate their job satisfaction on a scale of 1 (extremely low) to 10 (extremely high). On some days, the music had been at a slow tempo, others at a moderate tempo, and still others at a fast tempo. The following data represent an averaged score for 6 subjects across each condition. Subject A B C D E Slow 5 7 4 8 6 Music Condition (Tempo) Moderate 8 10 5 9 8 Fast 4 6 1 5 4 Conduct a One-Way Repeated Measures ANOVA at the .01 level; cover all elements on Handout. 3. Shranger (1972) conducted an experiment that examined the effect of an audience being present on the performance of two people with high self-esteem vs people with low self-esteem. Hypothetical data from this experiment are as follows. The dependent variable is the number of errors made by each subject. Self-esteem (Independent Variable B) High Low Audience Condition (Independent Variable A) Audience Alone 9 4 5 8 4 6 10 14 11 15 11 11 3 6 2 2 4 7 7 7 2 6 8 6 Conduct a full Two-Way ANOVA at = .05 given this 2 x 2 Factorial design; cover all elements on Handout. 4. Researchers studying the concept of eye-witness testimony wish to know whether recall of important information is influenced by the severity of the crime and the amount of time that passes before the witness is asked to recall important events. A videotape is made of a man stealing a woman's purse in an un-crowded clothing store. A second videotape is made, using the same actors, of a man using a gun to rob the cash register of the same clothing store. In this scenario, the woman is a sales clerk behind the cash register and there are two people standing at the counter. Subjects are asked to view the videotape and to imagine that they are at the crime scene. In the "immediate" condition, subjects are asked a series of questions about the crime within 10 minutes of viewing the videotape. In the "delay" condition, they are asked the same series of questions about the crime 30 minutes after viewing the tape. This is designed to be similar to an actual crime scene where there is some delay when taking witness statements. The dependent variable is the total number of questions answered correctly. Severity of Crime (Independent Variable B) Armed Robbery Purse-snatching Time Of Testing (Independent Variable A) Immediate Delay 7 5 7 7 6 6 7 5 6 7 7 7 8 8 8 8 7 8 9 7 I. 3 4 3 4 5 4 3 3 5 4 5 5 5 7 7 6 6 5 5 4 Conduct a full Two-Way ANOVA at = .01 given this 2 x 2 Factorial design; cover all elements on Handout. Math 001B Assignment 5.4 Name_________________________ DIRECTIONS To receive full credit, you must provide complete legible solutions to the following problems in the space provided. Transfer all your answers to the space provided on the test paper. 1. Find the general indefinite integral. (Use C for the constant of integration.) Ans____________________ 2. Find the general indefinite integral. (Use C for the constant of integration.) Ans____________________ 3. Set up a definite integral for the area of the region that lies to the right of the y-axis and to the left of the parabola Ans____________________ 4. Consider the function A= A(x) defined by , a. Find c. Find d. Draw both f(t) and A(x) on the same axis over the interval [0,3] 5. Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. The time is measured in seconds and the units for r(t) are tonnes (metric tons) per second. t 0 1 2 3 4 5 6 r(t) 2 10 24 36 46 54 60 a. Give upper and lower estimates for the total quantity Q(6) of erupted materials after 6 seconds. b. Use the Midpoint Rule to estimate Q(6) Math 001B Assignment 5.5 Name_________________________ DIRECTIONS To receive full credit, you must provide complete legible solutions to the following problems in the space provided. Transfer all your answers to the space provided on the test paper. 1. Use an appropriate substitution to evaluate the indefinite integrate Ans____________________ 2. Use an appropriate substitution to evaluate the indefinite integrate Ans____________________ 3. Use an appropriate substitution to evaluate the definite integral Ans____________________ 4. Use an appropriate substitution to evaluate the definite integral Ans____________________ 5. Use an appropriate substitution to evaluate the definite integral Ans____________________