he data below show the sport preference and age of participants from a random sample of members of a sports club. Test if sport preference is independent of age at the 0.02 significant level. H0: Sport preference is independent of age Ha: Sport preference is dependent on age 18-25 26-30 31-40 41 and over Tennis 40 56 57 46 Swimming 56 75 47 66 Basketball 74 60 67 47
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.
The data below show the sport preference and age of participants from a random sample of members of a sports club. Test if sport preference is independent of age at the 0.02 significant level.
H0: Sport preference is independent of age
Ha: Sport preference is dependent on age
| 18-25 | 26-30 | 31-40 | 41 and over | |
|---|---|---|---|---|
| Tennis | 40 | 56 | 57 | 46 |
| Swimming | 56 | 75 | 47 | 66 |
| Basketball | 74 | 60 | 67 | 47 |
a. Complete the table: Give all answers as decimals rounded to 4 places.
| Observed Frequency |
Expected Frequency |
(O−E)2E(O-E)2E |
|---|---|---|
| 40 | ||
| 56 | ||
| 57 | ||
| 46 | ||
| 56 | ||
| 75 | ||
| 47 | ||
| 66 | ||
| 74 | ||
| 60 | ||
| 67 | ||
| 47 | ||
| Total |
(b) What is the chi-square test-statistic for this data?
Test Statistic: χ2=χ2=
(d) The p-value is...
- less than (or equal to) αα
- greater than αα
(e) The p-value leads to a decision to...
- fail to reject the null
- reject the null
(f) What is the final conclusion?
a)There is not sufficient evidence to conclude sport preference is dependent on age.
b)There is sufficient evidence to conclude sport preference is dependent on age.
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