A researcher uses a matched-subjects design to investigate whether single people who own pets are generally happier than singles without pets. A mood inventory questionnaire is administered to a group of 20 to 29-year old non-pet owners and a similar age group of pet owners. The pet owners are matched one to one with the non-pet owners for income, number of close friendships, and general health. The data are as follows: MATCHED PAIR NON-PET OWNER PET OWNER A 12 14 B 8 7 C 10 13 D 9 9 E 7 13 F 10 12 Is there a significant difference in the mood scores for non-pet owners versus pet owners? Test with α = 0.05 for two tails. Construct the 95% confidence interval to estimate the size of the mean difference in mood between the population of pet owners and the population of non-pet owners. (You should find that a mean difference of µ = 0 is an acceptable value, which is consistent with the conclusion from the hypothesis test.)
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.
A researcher uses a matched-subjects design to investigate whether single people who own pets are generally happier than singles without pets. A mood inventory questionnaire is administered to a group of 20 to 29-year old non-pet owners and a similar age group of pet owners. The pet owners are matched one to one with the non-pet owners for income, number of close friendships, and general health. The data are as follows:
|
MATCHED PAIR |
NON-PET OWNER |
PET OWNER |
|
A |
12 |
14 |
|
B |
8 |
7 |
|
C |
10 |
13 |
|
D |
9 |
9 |
|
E |
7 |
13 |
|
F |
10 |
12 |
- Is there a significant difference in the mood scores for non-pet owners versus pet owners? Test with α = 0.05 for two tails.
- Construct the 95% confidence
interval to estimate the size of the mean difference in mood between the population of pet owners and the population of non-pet owners. (You should find that a mean difference of µ = 0 is an acceptable value, which is consistent with the conclusion from the hypothesis test.) - a) 1. H0: µ = 0; HA: µ ≠ 0.
- α = 0.05, two-sided test -> 0.025 per critical area; D.F. = 6 – 1 = 5. ->Critical t value = 2.57
|
PAIR |
D |
MD = (2 – 1 + 3 + 0 + 6 + 2)/6 = 2 s2D = [(2 – 2)2 + (2 – (–1))2 + (2 – 3)2 + (2 – 0)2 + (2 – 6)2 + (2 – 2)2]/(6 – 1) = 6 sMD = SQRT(6/6) = 1 TEST T VALUE = (2 – 0)/1 = 2 |
|
A |
12 – 14 = 2 |
|
|
B |
8 – 7 = -1 |
|
|
C |
10 – 13 = 3 |
|
|
D |
9 – 9 = 0 |
|
|
E |
7 – 13 = 6 |
|
|
F |
10 – 12 = 2 |
- 4) |2| < |2.57| -> FAIL TO REJECT H0.
- LOWER BOUND OF C.I. -> 2 – 2.57*1 = –0.57
UPPER BOUND OF C.I. -> 2 + 2.57*1 = 4.57
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