A searcher is interested in if there is a relationship between whether a student enjoys mathematics and whether they enjoy statistics. To test this, he collected a sample of students and asked them whether they enjoyed mathematics and whether they enjoyed statistics. The results were summarised in the table below. Maths: Maths: No Yes Stats: 70 49 Yes Stats: No 48 48 Determine whether there is a relationship between a student's enjoyment of mathematics and statistics. Use a 2.5% level of significance. a. Choose the answer : 1) Alternative Hypothesis: There isn't a relationship between a student's enjoyment of mathematics and statistics. 2) Alternative Hypothesis: There is a positive relationship between a student's enjoyment of mathematics and statistics. 3) Alternative Hypothesis: There is a negative relationship between a student's enjoyment of mathematics and statistics. b. What is the critical value for this test ? c. What is the expected number of students who enjoy statistics but not mathematics ? d. What is the expected number of students who do not enjoy statistics and mathematics ? e. What is the test statistic for this 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.
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