Question 4. Classify each variable as qualitative or quantitative. If it is quantitative, state whether the variable is discrete or continuous. a) Colour of hair b) Gender c) Year of birth d) Daily rainfall e) Favourite colour f) Examination grade g) Test result as a percentage

4. Repeated-measures ANOVA Suppose you are interested in studying whether temperature affects spatial reasoning abilities. You decide to test spatial reasoning using completion time scores for the paper-folding test with five people, repeating the test on each person with three different temperatures (40 degrees, 60 degrees, and 80 degrees Fahrenheit). In 4. Repeated-measures ANOVA Suppose you are interested in studying whether temperature affects spatial reasoning abilities. You decide to test spatial reasoning using completion time scores for the paper-folding test with five people, repeating the test on each person with three different temperatures (40 degrees, 60 degrees, and 80 degrees Fahrenheit). In this experiment, the null hypothesis is that: O The completion time mean for at least one temperature is different from another O There are no individual differences in the completion time means O There are no differences in the mean completion times among the temperatures compared The factor of interest is the , and the dependent variable is the The results of the study are presented in the following data table. All scores are times necessary to complete the paper-folding task, recorded in seconds. Temperature Participant 40 Degrees 60 Degrees 80 Degrees Participant Totals A 3.41 3.40 3.49 P = 10.30 n 5 B 3.29 3.47 3.25 P = 10.01 k 3 с 3.70 3.71 3.63 P = 11.04 N 15 D 3.68 4.08 P = 11.64 54.70 3.88 3.74 E 3.80 4.17 P = 11.71 ΣΥΣ 200.4864 T = 17.88 T = 18.83 T = 17.99 SS=0.2335 SS = 0.1858 SS= 0.4866 = = = = The three treatments in the experiment define three populations of interest. You use an ANOVA to test the hypothesis that the three population means are equal. Present the results of your analysis in the following ANOVA table by entering the missing df values and selecting the correct values for the missing SS, MS, and F entries. (Note: For best results, retain at least two additional decimal points throughout your calculations. Depending on the order in which you do these calculations and the number of digits you retain, you may find slight rounding differences in the last digit between your answers and the answer choices.) ANOVA Table Source SS df MS F Between treatments Within treatments 0.0755 0.1973 Between subjects Error 14 9 Total F Distribution Numerator Degrees of Freedom = 26 Denominator Degrees of Freedom = 26 0 5000 1 1.00 5000 2 3 5 7 8 F Use the Distributions tool to find the critical value for a = 0.05. The critical value is F = At a significance level of a = 0.05, evaluate the null hypothesis that the population means for all treatments are equal. The null hypothesis is conclude that temperature affects spatial reasoning abilities. You

2. Assassination is a type of covert action. Do you think assassination is an acceptable action or is an action that should be forbidden, never done? Explain your answer.

v MI 7. Let (r) = for r e A := (0,0) (i) Find the pointwise limit f off (ii) Show that each f, is bounded on A but the pointwise limit f of the sequence is not bounded on A. (ii) Decide whether or not the convergence in () is uniform, prove your claim. (iv) use the e-strip to prove your claim in (iii).

A solid disk, a hoop, and a solid sphere are released at the same time at the top of an inclined ramp. Each has mass M and radius R. They all roll without slipping. In what order (fastest to slowest) do they reach the bottom of the ramp, if the moments of inertia of the disk, hoop, and sphere are ½ MR2, MR2, and 2/5 MR2? A) disk, hoop, sphere B) disk, sphere, hoop C) sphere, hoop, disk D) hoop, sphere, disk E) sphere, disk, hoop

R W R3 ww 10 12 ww R2 1 Write down the Kirchhoff Junction equation and solve it for I; in terms of 12 and 13. Write the result here: Ij = write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and follows the perimeter of the circuit diagram clockwise. 0 write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and touches the components 10V, Ry, 4V, and Ry O The resistors in the circuit have the following values . - R2 • Ry=60 Ry=130 Solve for all the following (some answers may be negative); 11 - Amperes 12 Amperes 13 Amperes NOTE: Forthin

3. Find the area between the curve y = 2^x andthe chord joining the points (0,1) and (2,4). 4. Find the coordinates of the centroid bounded bythe curve y = x^3 and the line x = 2.