Q2. MANNWHITNEY As part of a product-testing program, a paint manufacturer painted 12 houses in a suburban community. Six of the houses were painted with the company’s own product, and the other 6 were painted with a competitor’s paint. After 5 years, a panel of homeowners inspected the 12 houses and ranked them according to how well the paint was holding up. The rankings are as follows: Company’s paint 1 3 4 5 7 8 Competitor paint 2 6 9 10 11 12 Do these data indicate a significant difference between two brands of paint? Test at a =.05
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Q2. MANNWHITNEY
As part of a product-testing program, a paint manufacturer painted 12 houses in a
suburban community. Six of the houses were painted with the company’s own
product, and the other 6 were painted with a competitor’s paint. After 5 years, a panel
of homeowners inspected the 12 houses and ranked them according to how well the
paint was holding up. The rankings are as follows:
Company’s paint 1 3 4 5 7 8
Competitor paint 2 6 9 10 11 12
Do these data indicate a significant difference between two brands of paint? Test at a
=.05
IN PICTURE I HAVE ATTACHED EXAMPLE Q AND SOLUTION THAT NEED TO BE FOLLOWED TO DO THIS QUESTION. THANK YOU
![1. The size of leaves taken from bramble bushes were measured to see if there is a difference between the size of
the leaves growing in full sunlight and those growing in the shade. Test the hypothesis using 0.05 level of
significance.
Width Of Leaf / Cm
Sunlight
6.0
4.8
5.1
5.5
4.1
5.3
4.5
5.1
Shade
6.5
5.5
6.3
7.2
6.8
5.5
5.9
5.5
STEP1 Ho: There is no difference between the two treatments. Therefore, there is no tendency for the
ranks in sunlight condition to be systematically higher (or lower) than the ranks in the shade condition.
H1: There is a difference between the two treatments. Therefore, the ranks in sunlight condition are
systematically higher (or lower) than the ranks in the shade condition.
Sunlight
RA
Shade
RB
6.0
12
6.5
14
STEP 2
4.8
3
5.5
8.5
5.1
4.5
6.3
13
5.5
8.5
7.2
16
4.1
1
6.8
15
5.3
5.5
8.5
4.5
2
5.9
11
5.1
4.5
5.5
8.5
ERA = 41.5
ERB = 94.5
a = .05
UA= NANB + [nA(nA+1)] /2 – ERA
= 8(8) + [8(8+1)] /2 – 41.5
nA = 8
= 58.5
UB = nAnB + [nB(nB+1)] / 2 – ERB
nB = 8
8(8) + [8(8+1)]/2 – 94.5
= 5.5
|
Ucritical = 13
STEP 4
STEP 3
U
min (UA, The original scores were ranked ordered and a Mann-Whitney U Test was used to compare the
UB)
ranks for the n
8 in sunlight condition and the n
8 in shade condition. The results indicate
= 5.5
significant difference between the two conditions, U = 5.5, with the sum of ranks equal to 41.5
5.5 < 13
for sunlight condition and 94.5 for shade condition. Therefore, the null hypothesis is rejected.
STEP 5
STEP 6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb7c09c8-3b49-4e8b-94ee-a031f37ce4c3%2Fc37c33ef-65d1-4548-928d-e73ec26398bc%2F5yvsa9_processed.png&w=3840&q=75)
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