STAT question

STAT 3300 Homework #8 Due Wednesday, 05/27/2020

Note: Answer these questions on a separate piece of paper. In the top right corner, include your name, SMU ID, and course number. Please include a title for the assignment so that it is clear to the graders. If you miss class the day the assignment is turned in, submit this before class in order to receive credit.

Question 1 (15 points total, 5 points each) For each of the following situations, find the degrees of freedom for the F statistic and then use R to calculate the p-value.

a) Six groups are being compared with five observations per group. The value of the F statistic is 2.47.

b) Four groups are being compared with 11 observations per group. The value of the F statistic is 5.03.

c) Five groups are being compared using 65 total observations. The value of the F statistic is 3.11.

Question 2 (30 points total, 10 points each) For each of the following situations, identify the response variable and the populations to be compared, and give c (the number of groups), ni, and N.

a) A developer of a virtual-reality (VR) teaching tool for the deaf wants to compare the effectiveness of different navigation methods. A total of 40 children were available for the experiment, of which equal numbers were randomly assigned to use a joystick, wand, dance mat, or gesture-based pinch gloves. The time (in seconds) to complete a designed VR path is recorded for each child.

b) To study the effects of pesticides on birds, an experimenter randomly (and equally) allocated 65 chicks to five diets (a control and four with a different pesticide included). After a month, the calcium content (milligrams) in a 1-centimeter length of bone from each chick was measured.

c) A university sandwich shop wants to compare the effects of providing free food with a sandwich order on sales. The experiment will be conducted from 11:00 A.M. to 2:00 P.M. for the next 20 weekdays. On each day, customers will be offered one of the following: a free drink, free chips, a free cookie, or nothing. Each option will be offered five times.

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Question 3 (20 points total) It is estimated that more than 90% of North American students use social media. This has prompted much research on the mental health impacts of these technologies. In one study, researchers investigated how mental health workers perceive the association between social media and mental disorders. A sample of psychiatrists from Canada completed a questionnaire, from which a perception score was obtained (a higher score indicating a stronger perceived association). The following ANOVA table summarizes a comparison of these scores across three age groups (generations).

Source DF SS MS F Age 2 137.78 68.89 0.45 Error 45 6899.54 153.32 Total 47 7037.32

a) (3 points) How many psychiatrists completed the questionnaire?

b) (6 points) What is the estimated common standard deviation?

c) (6 point) What is the p-value? Make sure to specify the degrees of freedom of the F statistic.

d) (5 points) State your conclusion using the p-value from part (c) and a 5% significance level.

Question 4 (35 points total) A group of technology students is interested in whether haptic feedback (forces and vibrations applied through a joystick) is helpful in navigating a simulated game environment they created. To investigate this, they randomly assign 20 students to each of three joystick controller types and record the time (seconds) it takes to complete a navigation mission. The joystick types are (1) a standard video game joystick, (2) a game joystick with force feedback, and (3) a game joystick with vibration feedback. Using the table below of group means and standard deviations, construct an ANOVA table (9 points, 1 per blank). Based on the F statistic and degrees of freedom, compute the p-value. What do you conclude (1 point)?

Joystick Group Mean Group SD n 1 279 78 20 2 245 68 20 3 258 80 20

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