A professor wants to know whether or not there is a difference in comprehension of a lab assignment among students depending on if the instructions are given all in text, or if they are given primarily with visual illustrations. She randomly divides her class into two groups of 15, gives one group instructions in text and the second group instructions with visual illustrations. The following data summarizes the scores the students received on a test given after the lab. Let the populations be normally distributed with a population standard deviation of 5.32 points for both the text and visual illustrations.
Text (Group 1)
Visual Illustrations (Group 2)
57.3
59.15
45.3
57.6
87.1
72.9
65.2
83.2
43.1
64
87.3
77.7
75.2
78.2
88.2
64.4
67.5
89
86.2
72.9
68.2
88.2
54.4
43.8
93
98.1
89.2
95.1
55
85.1
Is there evidence to suggest that a difference exists in the comprehension of the lab based on the test scores? Use α=0.05.
Enter the P-Value - round to 4 decimal places.
p-value =

There is evidence since we have to apply a two-tailed test

p-value = 0.0212

Step-by-step explanation:

Given data:

α=0.05.

population std = 5.32

A) To test if there is difference in the comprehension of the lab based on test scores at α = 0.05.  = 5%

we will apply a two-tailed test  ( Null and alternate hypothesis test )

H0 : u1 = u2

Ha : u1 ≠ u2

there is evidence since we have to apply a two-tailed test

B ) Determine the P-value for the test

attached below  a detailed solution ( solved using excel )

Z- test : two sample for means

p-value = 0.0212

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.