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Answer:
It is concluded that no difference exists in the comprehension of the lab based on the test scores.
Step-by-step explanation:
<em><u>Let the populations be normally distributed with a populations standard deviation of 5.32 points for both the text and visual illustrations.</u></em>
The above statement tells us that the independent t or two sample t test will be performed as both have equal variances and are normally distributed.
This can be easily done through excel.
The following table is obtained
t-Test: Two-Sample Assuming Equal Variances
<u> Text Visual Illustrations</u>
Mean 70.28 75.08
Variance 304.48 228.58
Observations 15 15
Pooled Variance Sp²= 266.53
Pooled Standard Deviation = Sp = 16.33
Hypothesized Mean Difference = x1`-x2`= 0
df = n1+n2-2= 15+15-2= 30-2= 28
t Stat -0.805188239
<u>P(T<=t) two-tail 0.427495979 </u>
<u>t Critical two-tail 1.701130908 </u>
Let the null and alternate hypotheses be
H0 : u1-u2= 0 against the claim Ha: u1-u2≠0
There is no difference between the means
against the claim
that there is a difference in means 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.
The significance level is ∝= 0.1
The d.f is n1+n2-2= 15+15-2= 30-2=28
This is a two tailed test and the critical region is t (0.025) (28) ≥ 1.7011 and t (0.025) (28) ≤ - 1.7011.
The test statistic is
t= x1-x2/ Sp √1/n1+ 1/n2
t= 70.28 -75.08/ 16.33√1/15 +1/15
t= -4.8/5.963
t= -0.8049811 ( minute difference from excel result due to rounding)
Since the calculated value of t= -0.8049 does not fall in the critical region we conclude that there is no difference in means 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.
We accept the null hypothesis.
The p- value is 0.427495979.
Answer:
Step-by-step explanation:
<u>slope-intercept </u><u>form</u>
y= mx +c, where m is the slope and c is the y-intercept
Given line: y= 2x +2
slope= 2
The product of the slopes of perpendicular lines is -1. Let the slope of the unknown line be m.
m(2)= -1
m= -1 ÷2
m= -½
Substitute the value of m into the equation:
y= -½x +c
To find the value of c, substitute a pair of coordinates.
When x= 4, y= 3,
3= -½(4) +c
3= -2 +c
c= 3 +2
c= 5
Thus, the equation of the line is y= -½x +5.
Answer:
it is true
Step-by-step explanation:
We can demonstrate this by contradiction.
First choosing a random rational and assuming that exist two ways to represent this rational. Call that rational x, a, b and a', b ' the couples of relatively prime to express x.
Then we have
Isolating a:
a is an integer and a' is a relatively prime with b', for this reason b has to be a factor of b'. Suppose this factorization b'=nb, replacing it:
But now we have that n is a factor of a and is a factor of b, it means that a and b are not relatively prime, that is a contradiction with our premises. The sentence is true.
And referring to the positive denominator. If we want to express a positive rational the denominator and numerator will be both positive and if is a negative one we choose a positive denominator and a negative numerator.