A researcher is interested in seeing if the average income of rural families is different than that of urban families. To see if his claim is correct he randomly selects 42 families from a rural area and finds that they have an average income of $68677 with a population standard deviation of $654. He then selects 46 families from a urban area and finds that they have an average income of $65929 with a population standard deviation of $665. Perform a hypothesis test using a significance level of 0.01 Let rural families be sample 1 and urban familis be sample 2. test his claim. The correct hypotheses are: O Ho: µ1 < H2 HA: H1 > H2(claim) Ο Η: μι > μ2 HA: H1 < µ2(claim) O Ho: µ1 = µ2 HA: H1 7 H2(claim) Since the level of significance is 0.01 the critical value is 2.576 and -2.576 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: O reject Ho O do not reject Ho The final conclusion is that: O There is enough evidence to reject the claim that the average income of rural families is different than that of urban families. O There is not enough evidence to reject the claim that the average income of rural families is different than that of urban families. O There is enough evidence to support the claim that the average income of rural families is different than that of urban families. O There is not enough evidence to support the claim that the average income of rural families is different than that of urban families.
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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